<?xml version="1.0" encoding="utf-8"?>
<!--XBRL document created with Toppan Merrill Bridge  10.6.2.5 -->
<!--Based on XBRL 2.1-->
<!--Created on: 5/7/2024 7:28:20 PM-->
<!--Modified on: 5/7/2024 7:28:20 PM-->
<link:linkbase xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:xbrldt="http://xbrl.org/2005/xbrldt">
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DocumentDocumentAndEntityInformation" roleURI="http://burtechacquisitioncorp.com/role/DocumentDocumentAndEntityInformation" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#StatementConsolidatedBalanceSheets" roleURI="http://burtechacquisitioncorp.com/role/StatementConsolidatedBalanceSheets" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#StatementConsolidatedBalanceSheetsParenthetical" roleURI="http://burtechacquisitioncorp.com/role/StatementConsolidatedBalanceSheetsParenthetical" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#StatementConsolidatedStatementsOfOperations" roleURI="http://burtechacquisitioncorp.com/role/StatementConsolidatedStatementsOfOperations" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#StatementConsolidatedStatementsOfChangesInStockholdersDeficit" roleURI="http://burtechacquisitioncorp.com/role/StatementConsolidatedStatementsOfChangesInStockholdersDeficit" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureDescriptionOfOrganizationAndBusinessOperationsDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureDescriptionOfOrganizationAndBusinessOperationsDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesReconciliationOfNetIncomePerCommonShareDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesReconciliationOfNetIncomePerCommonShareDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureInitialPublicOfferingDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureInitialPublicOfferingDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureInitialPublicOfferingCommonStockSubjectToRedemptionDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureInitialPublicOfferingCommonStockSubjectToRedemptionDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosurePrivatePlacementDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosurePrivatePlacementDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureRelatedPartyTransactionsFounderSharesDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureRelatedPartyTransactionsFounderSharesDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureRelatedPartyTransactionsAdditionalInformationDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureRelatedPartyTransactionsAdditionalInformationDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureCommitmentsAndContingenciesDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureCommitmentsAndContingenciesDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureStockholdersDeficitCommonStockSharesDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureStockholdersDeficitCommonStockSharesDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureStockholdersDeficitWarrantsDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureStockholdersDeficitWarrantsDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureFairValueMeasurementsDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureFairValueMeasurementsDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <roleRef xlink:type="simple" xlink:href="brkh-20231231.xsd#DisclosureSubsequentEventsDetails" roleURI="http://burtechacquisitioncorp.com/role/DisclosureSubsequentEventsDetails" xmlns="http://www.xbrl.org/2003/linkbase" />
  <link:roleRef roleURI="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-roles-2023.xsd#eedm" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://www.esma.europa.eu/xbrl/esef/arcrole/wider-narrower" xlink:type="simple" xlink:href="http://www.xbrl.org/lrr/arcrole/esma-arcrole-2018-11-21.xsd#wider-narrower" />
  <link:roleRef roleURI="http://burtechacquisitioncorp.com/role/DisclosureStandardAndCustomAxisDomainDefaults" xlink:href="brkh-20231231.xsd#DisclosureStandardAndCustomAxisDomainDefaults" xlink:type="simple" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/all" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#all" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-domain" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-domain" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/domain-member" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#domain-member" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/hypercube-dimension" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#hypercube-dimension" />
  <link:arcroleRef arcroleURI="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:type="simple" xlink:href="http://www.xbrl.org/2005/xbrldt-2005.xsd#dimension-default" />
  <link:definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureStandardAndCustomAxisDomainDefaults" xlink:type="extended" xlink:title="99900 - Disclosure - Standard And Custom Axis Domain Defaults">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis_1" xlink:title="us-gaap_StatementClassOfStockAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain_1" xlink:title="us-gaap_ClassOfStockDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_StatementClassOfStockAxis_1" xlink:to="us-gaap_ClassOfStockDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_StatementClassOfStockAxis_1 To us-gaap_ClassOfStockDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_1" xlink:title="us-gaap_SubsidiarySaleOfStockAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_1" xlink:title="us-gaap_SaleOfStockNameOfTransactionDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_SubsidiarySaleOfStockAxis_1" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_SubsidiarySaleOfStockAxis_1 To us-gaap_SaleOfStockNameOfTransactionDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis_1" xlink:title="us-gaap_StatementEquityComponentsAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain_1" xlink:title="us-gaap_EquityComponentDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_StatementEquityComponentsAxis_1" xlink:to="us-gaap_EquityComponentDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_StatementEquityComponentsAxis_1 To us-gaap_EquityComponentDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_1" xlink:title="us-gaap_ClassOfWarrantOrRightAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_1" xlink:title="us-gaap_ClassOfWarrantOrRightDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_ClassOfWarrantOrRightAxis_1" xlink:to="us-gaap_ClassOfWarrantOrRightDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_ClassOfWarrantOrRightAxis_1 To us-gaap_ClassOfWarrantOrRightDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LegalEntityAxis" xlink:label="dei_LegalEntityAxis_1" xlink:title="dei_LegalEntityAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityDomain" xlink:label="dei_EntityDomain_1" xlink:title="dei_EntityDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="dei_LegalEntityAxis_1" xlink:to="dei_EntityDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:dei_LegalEntityAxis_1 To dei_EntityDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1" xlink:title="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain_1" xlink:title="us-gaap_RelatedPartyDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1" xlink:to="us-gaap_RelatedPartyDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_1 To us-gaap_RelatedPartyDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis_1" xlink:title="us-gaap_RelatedPartyTransactionAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain_1" xlink:title="us-gaap_RelatedPartyTransactionDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_RelatedPartyTransactionAxis_1" xlink:to="us-gaap_RelatedPartyTransactionDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_RelatedPartyTransactionAxis_1 To us-gaap_RelatedPartyTransactionDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis_1" xlink:title="srt_StatementScenarioAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain_1" xlink:title="srt_ScenarioUnspecifiedDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="srt_StatementScenarioAxis_1" xlink:to="srt_ScenarioUnspecifiedDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:srt_StatementScenarioAxis_1 To srt_ScenarioUnspecifiedDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_1" xlink:title="us-gaap_FairValueByFairValueHierarchyLevelAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1" xlink:title="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis_1" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_FairValueByFairValueHierarchyLevelAxis_1 To us-gaap_FairValueMeasurementsFairValueHierarchyDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentAxis" xlink:label="us-gaap_FinancialInstrumentAxis_1" xlink:title="us-gaap_FinancialInstrumentAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_1" xlink:title="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_FinancialInstrumentAxis_1" xlink:to="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_FinancialInstrumentAxis_1 To us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementFrequencyAxis" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_1" xlink:title="us-gaap_FairValueByMeasurementFrequencyAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementFrequencyDomain" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_1" xlink:title="us-gaap_FairValueMeasurementFrequencyDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_FairValueByMeasurementFrequencyAxis_1" xlink:to="us-gaap_FairValueMeasurementFrequencyDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_FairValueByMeasurementFrequencyAxis_1 To us-gaap_FairValueMeasurementFrequencyDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeAxis" xlink:label="us-gaap_MeasurementInputTypeAxis_1" xlink:title="us-gaap_MeasurementInputTypeAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeDomain" xlink:label="us-gaap_MeasurementInputTypeDomain_1" xlink:title="us-gaap_MeasurementInputTypeDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_MeasurementInputTypeAxis_1" xlink:to="us-gaap_MeasurementInputTypeDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_MeasurementInputTypeAxis_1 To us-gaap_MeasurementInputTypeDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RestatementAxis" xlink:label="srt_RestatementAxis_1" xlink:title="srt_RestatementAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RestatementDomain" xlink:label="srt_RestatementDomain_1" xlink:title="srt_RestatementDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="srt_RestatementAxis_1" xlink:to="srt_RestatementDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:srt_RestatementAxis_1 To srt_RestatementDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxAuthorityAxis" xlink:label="us-gaap_IncomeTaxAuthorityAxis_1" xlink:title="us-gaap_IncomeTaxAuthorityAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxAuthorityDomain" xlink:label="us-gaap_IncomeTaxAuthorityDomain_1" xlink:title="us-gaap_IncomeTaxAuthorityDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_IncomeTaxAuthorityAxis_1" xlink:to="us-gaap_IncomeTaxAuthorityDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_IncomeTaxAuthorityAxis_1 To us-gaap_IncomeTaxAuthorityDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ProductOrServiceAxis" xlink:label="srt_ProductOrServiceAxis_1" xlink:title="srt_ProductOrServiceAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ProductsAndServicesDomain" xlink:label="srt_ProductsAndServicesDomain_1" xlink:title="srt_ProductsAndServicesDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="srt_ProductOrServiceAxis_1" xlink:to="srt_ProductsAndServicesDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:srt_ProductOrServiceAxis_1 To srt_ProductsAndServicesDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeAxis" xlink:label="srt_RangeAxis_1" xlink:title="srt_RangeAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeMember" xlink:label="srt_RangeMember_1" xlink:title="srt_RangeMember_1" />
    <link:definitionArc xlink:type="arc" xlink:from="srt_RangeAxis_1" xlink:to="srt_RangeMember_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:srt_RangeAxis_1 To srt_RangeMember_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis_1" xlink:title="us-gaap_SubsequentEventTypeAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain_1" xlink:title="us-gaap_SubsequentEventTypeDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_SubsequentEventTypeAxis_1" xlink:to="us-gaap_SubsequentEventTypeDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_SubsequentEventTypeAxis_1 To us-gaap_SubsequentEventTypeDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TypeOfArrangementAxis" xlink:label="us-gaap_TypeOfArrangementAxis_1" xlink:title="us-gaap_TypeOfArrangementAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_1" xlink:title="us-gaap_ArrangementsAndNonarrangementTransactionsMember_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_TypeOfArrangementAxis_1" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_TypeOfArrangementAxis_1 To us-gaap_ArrangementsAndNonarrangementTransactionsMember_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentAxis" xlink:label="us-gaap_DebtInstrumentAxis_1" xlink:title="us-gaap_DebtInstrumentAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain_1" xlink:title="us-gaap_DebtInstrumentNameDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_DebtInstrumentAxis_1" xlink:to="us-gaap_DebtInstrumentNameDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_DebtInstrumentAxis_1 To us-gaap_DebtInstrumentNameDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessAcquisitionAxis" xlink:label="us-gaap_BusinessAcquisitionAxis_1" xlink:title="us-gaap_BusinessAcquisitionAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessAcquisitionAcquireeDomain" xlink:label="us-gaap_BusinessAcquisitionAcquireeDomain_1" xlink:title="us-gaap_BusinessAcquisitionAcquireeDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_BusinessAcquisitionAxis_1" xlink:to="us-gaap_BusinessAcquisitionAcquireeDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:us-gaap_BusinessAcquisitionAxis_1 To us-gaap_BusinessAcquisitionAcquireeDomain_1" order="1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis_1" xlink:title="srt_CounterpartyNameAxis_1" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_1" xlink:title="srt_RepurchaseAgreementCounterpartyNameDomain_1" />
    <link:definitionArc xlink:type="arc" xlink:from="srt_CounterpartyNameAxis_1" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain_1" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-default" xlink:title="definition:srt_CounterpartyNameAxis_1 To srt_RepurchaseAgreementCounterpartyNameDomain_1" order="1" />
  </link:definitionLink>
  <link:definitionLink xlink:role="http://fasb.org/us-gaap/role/eedm/ExtensibleEnumerationLists" xlink:type="extended" xlink:title="Extensible Enumeration Domain Members">
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain_3" xlink:title="us-gaap_RelatedPartyDomain_3" />
    <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember_3" xlink:title="us-gaap_RelatedPartyMember_3" />
    <link:definitionArc xlink:type="arc" xlink:from="us-gaap_RelatedPartyDomain_3" xlink:to="us-gaap_RelatedPartyMember_3" use="optional" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" xlink:title="definition:us-gaap_RelatedPartyDomain_3 To us-gaap_RelatedPartyMember_3" order="1" priority="0" />
  </link:definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DocumentDocumentAndEntityInformation" xlink:type="extended" xlink:title="00090 - Document - Document and Entity Information" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentInformationTable" xlink:label="dei_DocumentInformationTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="dei_DocumentInformationTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_UnitsEachConsistingOfOneShareOfClassaCommonStockAndOneRedeemableWarrantToPurchaseOneShareOfClassCommonStockFor11.50PerShareMember" xlink:label="brkh_UnitsEachConsistingOfOneShareOfClassaCommonStockAndOneRedeemableWarrantToPurchaseOneShareOfClassCommonStockFor11.50PerShareMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="brkh_UnitsEachConsistingOfOneShareOfClassaCommonStockAndOneRedeemableWarrantToPurchaseOneShareOfClassCommonStockFor11.50PerShareMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_WarrantsEachWholeWarrantExercisableForOneShareOfClassCommonStockAtExercisePriceMember" xlink:label="brkh_WarrantsEachWholeWarrantExercisableForOneShareOfClassCommonStockAtExercisePriceMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="brkh_WarrantsEachWholeWarrantExercisableForOneShareOfClassCommonStockAtExercisePriceMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentInformationLineItems" xlink:label="dei_DocumentInformationLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentInformationTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType" xlink:label="dei_DocumentType" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentType" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentAnnualReport" xlink:label="dei_DocumentAnnualReport" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentAnnualReport" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentTransitionReport" xlink:label="dei_DocumentTransitionReport" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentTransitionReport" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate" xlink:label="dei_DocumentPeriodEndDate" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentPeriodEndDate" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFileNumber" xlink:label="dei_EntityFileNumber" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityFileNumber" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityRegistrantName" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode" xlink:label="dei_EntityIncorporationStateCountryCode" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityIncorporationStateCountryCode" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityTaxIdentificationNumber" xlink:label="dei_EntityTaxIdentificationNumber" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityTaxIdentificationNumber" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1" xlink:label="dei_EntityAddressAddressLine1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityAddressAddressLine1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown" xlink:label="dei_EntityAddressCityOrTown" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityAddressCityOrTown" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressStateOrProvince" xlink:label="dei_EntityAddressStateOrProvince" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityAddressStateOrProvince" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode" xlink:label="dei_EntityAddressPostalZipCode" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityAddressPostalZipCode" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode" xlink:label="dei_CityAreaCode" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_CityAreaCode" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber" xlink:label="dei_LocalPhoneNumber" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="15" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_LocalPhoneNumber" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle" xlink:label="dei_Security12bTitle" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="16" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_Security12bTitle" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol" xlink:label="dei_TradingSymbol" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="17" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_TradingSymbol" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName" xlink:label="dei_SecurityExchangeName" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="18" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_SecurityExchangeName" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCurrentReportingStatus" xlink:label="dei_EntityCurrentReportingStatus" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="19" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityCurrentReportingStatus" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInteractiveDataCurrent" xlink:label="dei_EntityInteractiveDataCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="20" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityInteractiveDataCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFilerCategory" xlink:label="dei_EntityFilerCategory" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="21" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityFilerCategory" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitySmallBusiness" xlink:label="dei_EntitySmallBusiness" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="22" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntitySmallBusiness" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany" xlink:label="dei_EntityEmergingGrowthCompany" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="23" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityEmergingGrowthCompany" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityWellKnownSeasonedIssuer" xlink:label="dei_EntityWellKnownSeasonedIssuer" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="24" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityWellKnownSeasonedIssuer" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityVoluntaryFilers" xlink:label="dei_EntityVoluntaryFilers" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="25" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityVoluntaryFilers" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_IcfrAuditorAttestationFlag" xlink:label="dei_IcfrAuditorAttestationFlag" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="26" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_IcfrAuditorAttestationFlag" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFinStmtErrorCorrectionFlag" xlink:label="dei_DocumentFinStmtErrorCorrectionFlag" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="27" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentFinStmtErrorCorrectionFlag" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityExTransitionPeriod" xlink:label="dei_EntityExTransitionPeriod" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="28" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityExTransitionPeriod" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityShellCompany" xlink:label="dei_EntityShellCompany" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="29" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityShellCompany" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityPublicFloat" xlink:label="dei_EntityPublicFloat" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="30" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityPublicFloat" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCommonStockSharesOutstanding" xlink:label="dei_EntityCommonStockSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="31" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityCommonStockSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AuditorName" xlink:label="dei_AuditorName" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="32" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_AuditorName" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AuditorLocation" xlink:label="dei_AuditorLocation" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="33" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_AuditorLocation" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AuditorFirmId" xlink:label="dei_AuditorFirmId" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="34" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_AuditorFirmId" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey" xlink:label="dei_EntityCentralIndexKey" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="35" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_EntityCentralIndexKey" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CurrentFiscalYearEndDate" xlink:label="dei_CurrentFiscalYearEndDate" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="36" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_CurrentFiscalYearEndDate" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalYearFocus" xlink:label="dei_DocumentFiscalYearFocus" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="37" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentFiscalYearFocus" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalPeriodFocus" xlink:label="dei_DocumentFiscalPeriodFocus" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="38" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_DocumentFiscalPeriodFocus" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag" xlink:label="dei_AmendmentFlag" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="39" xlink:from="dei_DocumentInformationLineItems" xlink:to="dei_AmendmentFlag" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/StatementConsolidatedBalanceSheets" xlink:type="extended" xlink:title="00100 - Statement - CONSOLIDATED BALANCE SHEETS" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsAbstract" xlink:label="us-gaap_AssetsAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_AssetsAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrentAbstract" xlink:label="us-gaap_AssetsCurrentAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsCurrentAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_CashAndCashEquivalentsAtCarryingValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_RestrictedCashCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueFromSponsorCurrent" xlink:label="brkh_DueFromSponsorCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="brkh_DueFromSponsorCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrustCurrent" xlink:label="us-gaap_AssetsHeldInTrustCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsHeldInTrustCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssetsCurrent" xlink:label="us-gaap_OtherAssetsCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_OtherAssetsCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrent" xlink:label="us-gaap_AssetsCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_AssetsCurrentAbstract" xlink:to="us-gaap_AssetsCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrustNoncurrent" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets" xlink:label="us-gaap_Assets" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_AssetsAbstract" xlink:to="us-gaap_Assets" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_LiabilitiesAndStockholdersEquityAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrentAbstract" xlink:label="us-gaap_LiabilitiesCurrentAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesCurrentAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedLiabilitiesCurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_AccruedLiabilitiesCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FranchiseTaxPayable" xlink:label="brkh_FranchiseTaxPayable" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="brkh_FranchiseTaxPayable" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueToTrustAccountCurrent" xlink:label="brkh_DueToTrustAccountCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="brkh_DueToTrustAccountCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PayableCommonStockRedeemed" xlink:label="us-gaap_PayableCommonStockRedeemed" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_PayableCommonStockRedeemed" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableCurrent" xlink:label="us-gaap_NotesPayableCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_NotesPayableCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedIncomeTaxesCurrent" xlink:label="us-gaap_AccruedIncomeTaxesCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_AccruedIncomeTaxesCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SalesAndExciseTaxPayableCurrent" xlink:label="us-gaap_SalesAndExciseTaxPayableCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_SalesAndExciseTaxPayableCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrent" xlink:label="us-gaap_LiabilitiesCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_LiabilitiesCurrentAbstract" xlink:to="us-gaap_LiabilitiesCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DeferredOfferingCostsNoncurrent" xlink:label="brkh_DeferredOfferingCostsNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="brkh_DeferredOfferingCostsNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Liabilities" xlink:label="us-gaap_Liabilities" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_Liabilities" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingencies" xlink:label="us-gaap_CommitmentsAndContingencies" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_CommitmentsAndContingencies" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityAbstract" xlink:label="us-gaap_StockholdersEquityAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquityAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockValue" xlink:label="us-gaap_PreferredStockValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_PreferredStockValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockValue" xlink:label="us-gaap_CommonStockValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_CommonStockValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsAccumulatedDeficit" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_RetainedEarningsAccumulatedDeficit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_StockholdersEquityAbstract" xlink:to="us-gaap_StockholdersEquity" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquity" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="us-gaap_LiabilitiesAndStockholdersEquity" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/StatementConsolidatedBalanceSheetsParenthetical" xlink:type="extended" xlink:title="00105 - Statement - CONSOLIDATED BALANCE SHEETS (Parenthetical)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_TemporaryEquitySharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityRedemptionPricePerShare" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_TemporaryEquityRedemptionPricePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockParOrStatedValuePerShare" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_PreferredStockParOrStatedValuePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesAuthorized" xlink:label="us-gaap_PreferredStockSharesAuthorized" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_PreferredStockSharesAuthorized" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesOutstanding" xlink:label="us-gaap_PreferredStockSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_PreferredStockSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesIssued" xlink:label="us-gaap_PreferredStockSharesIssued" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_PreferredStockSharesIssued" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesAuthorized" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_CommonStockSharesIssued" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/StatementConsolidatedStatementsOfOperations" xlink:type="extended" xlink:title="00200 - Statement - CONSOLIDATED STATEMENTS OF OPERATIONS" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingCostsAndExpenses" xlink:label="us-gaap_OperatingCostsAndExpenses" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_OperatingCostsAndExpenses" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FranchiseTaxExpense" xlink:label="brkh_FranchiseTaxExpense" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_StatementLineItems" xlink:to="brkh_FranchiseTaxExpense" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingIncomeLoss" xlink:label="us-gaap_OperatingIncomeLoss" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_OperatingIncomeLoss" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NonoperatingIncomeExpenseAbstract" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_NonoperatingIncomeExpenseAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentIncomeInterest" xlink:label="us-gaap_InvestmentIncomeInterest" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_InvestmentIncomeInterest" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NonoperatingIncomeExpense" xlink:label="us-gaap_NonoperatingIncomeExpense" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_NonoperatingIncomeExpense" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxExpenseBenefit" xlink:label="us-gaap_IncomeTaxExpenseBenefit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="us-gaap_IncomeTaxExpenseBenefit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_NetIncomeLoss" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_EarningsPerShareBasic" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_EarningsPerShareDiluted" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/StatementConsolidatedStatementsOfChangesInStockholdersDeficit" xlink:type="extended" xlink:title="00300 - Statement - CONSOLIDATED STATEMENTS OF CHANGES IN STOCKHOLDERS' DEFICIT" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable" xlink:label="us-gaap_StatementTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis" xlink:label="us-gaap_StatementEquityComponentsAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_StatementTable" xlink:to="us-gaap_StatementEquityComponentsAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityComponentDomain" xlink:label="us-gaap_EquityComponentDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementEquityComponentsAxis" xlink:to="us-gaap_EquityComponentDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockMember" xlink:label="us-gaap_CommonStockMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_CommonStockMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalMember" xlink:label="us-gaap_AdditionalPaidInCapitalMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_AdditionalPaidInCapitalMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsMember" xlink:label="us-gaap_RetainedEarningsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_EquityComponentDomain" xlink:to="us-gaap_RetainedEarningsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems" xlink:label="us-gaap_StatementLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_StatementTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_StatementLineItems" xlink:to="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquity" xlink:label="us-gaap_StockholdersEquity" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_StockholdersEquity" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharesIssued" xlink:label="us-gaap_SharesIssued" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_SharesIssued" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" xlink:label="brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_StockIssuedDuringPeriodValueConversionFromOneClassOfStockToAnother" xlink:label="brkh_StockIssuedDuringPeriodValueConversionFromOneClassOfStockToAnother" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="brkh_StockIssuedDuringPeriodValueConversionFromOneClassOfStockToAnother" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_EquityFairValueStockholderNonRedemptionAgreement" xlink:label="brkh_EquityFairValueStockholderNonRedemptionAgreement" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="brkh_EquityFairValueStockholderNonRedemptionAgreement" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_EquityStockholderNonRedemptionAgreement" xlink:label="brkh_EquityStockholderNonRedemptionAgreement" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="brkh_EquityStockholderNonRedemptionAgreement" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ExciseTaxLiabilityArisingFromRedemptionOfOrdinaryShares" xlink:label="brkh_ExciseTaxLiabilityArisingFromRedemptionOfOrdinaryShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="brkh_ExciseTaxLiabilityArisingFromRedemptionOfOrdinaryShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" xlink:label="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_TemporaryEquityAccretionToRedemptionValueAdjustment" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss" xlink:label="us-gaap_NetIncomeLoss" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="us-gaap_NetIncomeLoss" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureDescriptionOfOrganizationAndBusinessOperationsDetails" xlink:type="extended" xlink:title="40101 - Disclosure - DESCRIPTION OF ORGANIZATION AND BUSINESS OPERATIONS (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SponsorMember" xlink:label="brkh_SponsorMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyMember" xlink:to="brkh_SponsorMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_RelatedPartyTransactionAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_RelatedPartyLoansMember" xlink:label="brkh_RelatedPartyLoansMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_RelatedPartyLoansMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PromissoryNoteWithRelatedPartyMember" xlink:label="brkh_PromissoryNoteWithRelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_PromissoryNoteWithRelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_SubsidiarySaleOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_IPOMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OverAllotmentOptionMember" xlink:label="us-gaap_OverAllotmentOptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_OverAllotmentOptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="4" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TypeOfArrangementAxis" xlink:label="us-gaap_TypeOfArrangementAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="5" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_TypeOfArrangementAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_TypeOfArrangementAxis" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NonRedemptionAgreementsMember" xlink:label="brkh_NonRedemptionAgreementsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="brkh_NonRedemptionAgreementsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SecondTrustAmendmentMember" xlink:label="brkh_SecondTrustAmendmentMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="brkh_SecondTrustAmendmentMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="6" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_ClassOfWarrantOrRightAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantMember" xlink:label="us-gaap_WarrantMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="us-gaap_WarrantMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PrivatePlacementWarrantsMember" xlink:label="brkh_PrivatePlacementWarrantsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_WarrantMember" xlink:to="brkh_PrivatePlacementWarrantsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PublicWarrantsMember" xlink:label="brkh_PublicWarrantsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_WarrantMember" xlink:to="brkh_PublicWarrantsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockLineItems" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ConditionForFutureBusinessCombinationNumberOfBusinessesMinimum" xlink:label="brkh_ConditionForFutureBusinessCombinationNumberOfBusinessesMinimum" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_ConditionForFutureBusinessCombinationNumberOfBusinessesMinimum" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSubsidiaries" xlink:label="brkh_NumberOfSubsidiaries" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_NumberOfSubsidiaries" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_UnitsIssuedDuringPeriodSharesNewIssues" xlink:label="brkh_UnitsIssuedDuringPeriodSharesNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_UnitsIssuedDuringPeriodSharesNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_SharesIssuedPricePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MinimumNetTangibleAssetsRequiredToConsummateBusinessCombination" xlink:label="brkh_MinimumNetTangibleAssetsRequiredToConsummateBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_MinimumNetTangibleAssetsRequiredToConsummateBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesIssuedPerUnit" xlink:label="brkh_NumberOfSharesIssuedPerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_NumberOfSharesIssuedPerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" xlink:label="brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfWarrants" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_ProceedsFromIssuanceOfWarrants" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TransactionCosts" xlink:label="brkh_TransactionCosts" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_TransactionCosts" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SaleOfStockUnderwritingFees" xlink:label="brkh_SaleOfStockUnderwritingFees" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="brkh_TransactionCosts" xlink:to="brkh_SaleOfStockUnderwritingFees" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DeferredOfferingCostsNoncurrent" xlink:label="brkh_DeferredOfferingCostsNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_TransactionCosts" xlink:to="brkh_DeferredOfferingCostsNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FairValueOfSharesIssuedToUnderwriters" xlink:label="brkh_FairValueOfSharesIssuedToUnderwriters" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_TransactionCosts" xlink:to="brkh_FairValueOfSharesIssuedToUnderwriters" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SaleOfStockOtherOfferingCosts" xlink:label="brkh_SaleOfStockOtherOfferingCosts" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_TransactionCosts" xlink:to="brkh_SaleOfStockOtherOfferingCosts" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrust" xlink:label="us-gaap_AssetsHeldInTrust" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_AssetsHeldInTrust" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ConditionForFutureBusinessCombinationUseOfProceedsPercentage" xlink:label="brkh_ConditionForFutureBusinessCombinationUseOfProceedsPercentage" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="15" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_ConditionForFutureBusinessCombinationUseOfProceedsPercentage" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PaymentsForInvestmentOfCashInTrustAccount" xlink:label="brkh_PaymentsForInvestmentOfCashInTrustAccount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="16" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_PaymentsForInvestmentOfCashInTrustAccount" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_InvestmentsMaximumMaturityTerm" xlink:label="brkh_InvestmentsMaximumMaturityTerm" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="17" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_InvestmentsMaximumMaturityTerm" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumAllowedDissolutionExpenses" xlink:label="brkh_MaximumAllowedDissolutionExpenses" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="18" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_MaximumAllowedDissolutionExpenses" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PercentageObligationToRedeemPublicSharesIfEntityDoesNotCompleteBusinessCombination" xlink:label="brkh_PercentageObligationToRedeemPublicSharesIfEntityDoesNotCompleteBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="19" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_PercentageObligationToRedeemPublicSharesIfEntityDoesNotCompleteBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MonthsToCompleteAcquisitions" xlink:label="brkh_MonthsToCompleteAcquisitions" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="20" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_MonthsToCompleteAcquisitions" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumNumberOfSharesNotForRedemption" xlink:label="brkh_MaximumNumberOfSharesNotForRedemption" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="21" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_MaximumNumberOfSharesNotForRedemption" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" xlink:label="brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="22" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodShares" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="23" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodValue" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="24" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityRedemptionPricePerShare" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="25" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_TemporaryEquityRedemptionPricePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="26" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_TemporaryEquitySharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrustNoncurrent" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="27" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfTimesEntityHasRightToExtendBusinessCombinationForAdditionalMonth" xlink:label="brkh_NumberOfTimesEntityHasRightToExtendBusinessCombinationForAdditionalMonth" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="28" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_NumberOfTimesEntityHasRightToExtendBusinessCombinationForAdditionalMonth" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AdditionalTermToCompleteBusinessCombination" xlink:label="brkh_AdditionalTermToCompleteBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="29" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_AdditionalTermToCompleteBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AmountPerUnredeemedShareDepositedIntoTrustAccount" xlink:label="brkh_AmountPerUnredeemedShareDepositedIntoTrustAccount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="30" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_AmountPerUnredeemedShareDepositedIntoTrustAccount" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DepositToTrustAccountExtensionPaymentPerMonth" xlink:label="brkh_DepositToTrustAccountExtensionPaymentPerMonth" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="31" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_DepositToTrustAccountExtensionPaymentPerMonth" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="32" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_RestrictedCashCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueFromSponsorCurrent" xlink:label="brkh_DueFromSponsorCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="33" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_DueFromSponsorCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DepositInTrustAccount" xlink:label="brkh_DepositInTrustAccount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="34" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_DepositInTrustAccount" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="35" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PayableCommonStockRedeemed" xlink:label="us-gaap_PayableCommonStockRedeemed" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="36" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_PayableCommonStockRedeemed" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentIncomeInterest" xlink:label="us-gaap_InvestmentIncomeInterest" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="37" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_InvestmentIncomeInterest" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="38" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableCurrent" xlink:label="us-gaap_NotesPayableCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="39" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_NotesPayableCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableCurrentRelatedPartyTypeExtensibleEnumeration" xlink:label="us-gaap_NotesPayableCurrentRelatedPartyTypeExtensibleEnumeration" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="40" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_NotesPayableCurrentRelatedPartyTypeExtensibleEnumeration" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCredit" xlink:label="us-gaap_LineOfCredit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="41" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_LineOfCredit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromRelatedPartyDebt" xlink:label="us-gaap_ProceedsFromRelatedPartyDebt" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="42" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_ProceedsFromRelatedPartyDebt" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" xlink:label="brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="43" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" xlink:label="brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="44" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesDetails" xlink:type="extended" xlink:title="40201 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DisclosureOfAccountingPoliciesTable" xlink:label="brkh_DisclosureOfAccountingPoliciesTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="brkh_DisclosureOfAccountingPoliciesTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="brkh_DisclosureOfAccountingPoliciesTable" xlink:to="us-gaap_SubsidiarySaleOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_IPOMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:label="brkh_SummaryOfSignificantAccountingPoliciesLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="brkh_DisclosureOfAccountingPoliciesTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Cash" xlink:label="us-gaap_Cash" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_Cash" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashEquivalentsAtCarryingValue" xlink:label="us-gaap_CashEquivalentsAtCarryingValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_CashEquivalentsAtCarryingValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_RestrictedCashCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrust" xlink:label="us-gaap_AssetsHeldInTrust" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_AssetsHeldInTrust" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrustCurrent" xlink:label="us-gaap_AssetsHeldInTrustCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_AssetsHeldInTrustCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_TemporaryEquitySharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TransactionCosts" xlink:label="brkh_TransactionCosts" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="brkh_TransactionCosts" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SaleOfStockUnderwritingFees" xlink:label="brkh_SaleOfStockUnderwritingFees" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="brkh_TransactionCosts" xlink:to="brkh_SaleOfStockUnderwritingFees" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DeferredOfferingCostsNoncurrent" xlink:label="brkh_DeferredOfferingCostsNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_TransactionCosts" xlink:to="brkh_DeferredOfferingCostsNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FairValueOfSharesIssuedToUnderwriters" xlink:label="brkh_FairValueOfSharesIssuedToUnderwriters" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_TransactionCosts" xlink:to="brkh_FairValueOfSharesIssuedToUnderwriters" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SaleOfStockOtherOfferingCosts" xlink:label="brkh_SaleOfStockOtherOfferingCosts" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_TransactionCosts" xlink:to="brkh_SaleOfStockOtherOfferingCosts" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnrecognizedTaxBenefits" xlink:label="us-gaap_UnrecognizedTaxBenefits" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_UnrecognizedTaxBenefits" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" xlink:label="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_UnrecognizedTaxBenefitsIncomeTaxPenaltiesAndInterestAccrued" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="brkh_SummaryOfSignificantAccountingPoliciesLineItems" xlink:to="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureBasisOfPresentationAndSummaryOfSignificantAccountingPoliciesReconciliationOfNetIncomePerCommonShareDetails" xlink:type="extended" xlink:title="40202 - Disclosure - BASIS OF PRESENTATION AND SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES - Reconciliation of Net Income per Common Share (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:label="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" xlink:to="us-gaap_StatementClassOfStockAxis" priority="2" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassBCommonStockNotSubjectToRedemptionMember" xlink:label="brkh_ClassBCommonStockNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="brkh_ClassBCommonStockNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockLineItems" xlink:label="us-gaap_SubsidiarySaleOfStockLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_SubsidiaryOrEquityMethodInvesteeSaleOfStockBySubsidiaryOrEquityInvesteeTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityNetIncome" xlink:label="us-gaap_TemporaryEquityNetIncome" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_TemporaryEquityNetIncome" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:label="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic" xlink:label="us-gaap_EarningsPerShareBasic" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_EarningsPerShareBasic" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareDiluted" xlink:label="us-gaap_EarningsPerShareDiluted" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_SubsidiarySaleOfStockLineItems" xlink:to="us-gaap_EarningsPerShareDiluted" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureInitialPublicOfferingDetails" xlink:type="extended" xlink:title="40301 - Disclosure - INITIAL PUBLIC OFFERING (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_InitialPublicOfferingTable" xlink:label="brkh_InitialPublicOfferingTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="brkh_InitialPublicOfferingTable" xlink:to="us-gaap_SubsidiarySaleOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IPOMember" xlink:label="us-gaap_IPOMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_IPOMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OverAllotmentOptionMember" xlink:label="us-gaap_OverAllotmentOptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_OverAllotmentOptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_InitialPublicOfferingLineItems" xlink:label="brkh_InitialPublicOfferingLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_InitialPublicOfferingTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_UnitsIssuedDuringPeriodSharesNewIssues" xlink:label="brkh_UnitsIssuedDuringPeriodSharesNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_UnitsIssuedDuringPeriodSharesNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_UnitPrice" xlink:label="brkh_UnitPrice" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_UnitPrice" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesIssuedPerUnit" xlink:label="brkh_NumberOfSharesIssuedPerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_NumberOfSharesIssuedPerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfWarrantsIssuedPerUnit" xlink:label="brkh_NumberOfWarrantsIssuedPerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_NumberOfWarrantsIssuedPerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" xlink:label="brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_ProceedsFromTrustAccountUsedToPayFranchiseAndIncomeTaxes" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashCurrent" xlink:label="us-gaap_RestrictedCashCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="us-gaap_RestrictedCashCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueFromSponsorCurrent" xlink:label="brkh_DueFromSponsorCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_DueFromSponsorCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" xlink:label="brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_CashWithdrawnFromTrustAccountUsedForOperatingExpenses" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureInitialPublicOfferingCommonStockSubjectToRedemptionDetails" xlink:type="extended" xlink:title="40302 - Disclosure - INITIAL PUBLIC OFFERING - Common stock subject to redemption (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_InitialPublicOfferingTable" xlink:label="brkh_InitialPublicOfferingTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="brkh_InitialPublicOfferingTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_InitialPublicOfferingLineItems" xlink:label="brkh_InitialPublicOfferingLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_InitialPublicOfferingTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:label="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="us-gaap_TemporaryEquityCarryingAmountAttributableToParent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AccretionOfCarryingValueToRedemptionValue" xlink:label="brkh_AccretionOfCarryingValueToRedemptionValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_AccretionOfCarryingValueToRedemptionValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedOrCalledDuringPeriodValue" xlink:label="brkh_TemporaryEquityStockRedeemedOrCalledDuringPeriodValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_InitialPublicOfferingLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedOrCalledDuringPeriodValue" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosurePrivatePlacementDetails" xlink:type="extended" xlink:title="40401 - Disclosure - PRIVATE PLACEMENT (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PrivatePlacementTable" xlink:label="brkh_PrivatePlacementTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis" xlink:label="us-gaap_SubsidiarySaleOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="brkh_PrivatePlacementTable" xlink:to="us-gaap_SubsidiarySaleOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsidiarySaleOfStockAxis" xlink:to="us-gaap_SaleOfStockNameOfTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PrivatePlacementMember" xlink:label="us-gaap_PrivatePlacementMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="us-gaap_PrivatePlacementMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="brkh_PrivatePlacementTable" xlink:to="us-gaap_ClassOfWarrantOrRightAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PrivatePlacementWarrantsMember" xlink:label="brkh_PrivatePlacementWarrantsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="brkh_PrivatePlacementWarrantsMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PrivatePlacementLineItems" xlink:label="brkh_PrivatePlacementLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="brkh_PrivatePlacementTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" xlink:label="brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="brkh_ClassOfWarrantOrRightPriceOfWarrantsOrRights" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfWarrants" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="us-gaap_ProceedsFromIssuanceOfWarrants" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesIssuedPerUnit" xlink:label="brkh_NumberOfSharesIssuedPerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="brkh_NumberOfSharesIssuedPerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfWarrantsIssuedPerUnit" xlink:label="brkh_NumberOfWarrantsIssuedPerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="brkh_NumberOfWarrantsIssuedPerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="brkh_PrivatePlacementLineItems" xlink:to="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureRelatedPartyTransactionsFounderSharesDetails" xlink:type="extended" xlink:title="40501 - Disclosure - RELATED PARTY TRANSACTIONS - Founder Shares (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FounderSharesMember" xlink:label="brkh_FounderSharesMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_FounderSharesMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SponsorMember" xlink:label="brkh_SponsorMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyMember" xlink:to="brkh_SponsorMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AggregateNumberOfSharesOwned" xlink:label="brkh_AggregateNumberOfSharesOwned" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_AggregateNumberOfSharesOwned" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesSubjectToForfeiture" xlink:label="brkh_NumberOfSharesSubjectToForfeiture" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_NumberOfSharesSubjectToForfeiture" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesNotSubjectToForfeiture" xlink:label="brkh_NumberOfSharesNotSubjectToForfeiture" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_NumberOfSharesNotSubjectToForfeiture" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PercentageOfIssuedAndOutstandingSharesAfterInitialPublicOfferingCollectivelyHeldByInitialStockholders" xlink:label="brkh_PercentageOfIssuedAndOutstandingSharesAfterInitialPublicOfferingCollectivelyHeldByInitialStockholders" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_PercentageOfIssuedAndOutstandingSharesAfterInitialPublicOfferingCollectivelyHeldByInitialStockholders" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" xlink:label="brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" xlink:label="brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:label="brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureRelatedPartyTransactionsAdditionalInformationDetails" xlink:type="extended" xlink:title="40502 - Disclosure - RELATED PARTY TRANSACTIONS - Additional Information (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:label="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PromissoryNoteWithRelatedPartyMember" xlink:label="brkh_PromissoryNoteWithRelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_PromissoryNoteWithRelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AdministrativeSupportAgreementMember" xlink:label="brkh_AdministrativeSupportAgreementMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_AdministrativeSupportAgreementMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_RelatedPartyLoansMember" xlink:label="brkh_RelatedPartyLoansMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_RelatedPartyLoansMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SponsorMember" xlink:label="brkh_SponsorMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyMember" xlink:to="brkh_SponsorMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_ClassOfWarrantOrRightAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_WorkingCapitalLoansWarrantMember" xlink:label="brkh_WorkingCapitalLoansWarrantMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="brkh_WorkingCapitalLoansWarrantMember" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentAxis" xlink:label="us-gaap_DebtInstrumentAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="4" xlink:from="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="us-gaap_DebtInstrumentAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentNameDomain" xlink:label="us-gaap_DebtInstrumentNameDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_DebtInstrumentAxis" xlink:to="us-gaap_DebtInstrumentNameDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ConvertibleNotesPayableMember" xlink:label="us-gaap_ConvertibleNotesPayableMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_DebtInstrumentNameDomain" xlink:to="us-gaap_ConvertibleNotesPayableMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionLineItems" xlink:label="us-gaap_RelatedPartyTransactionLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_RelatedPartyTransactionExpensesFromTransactionsWithRelatedPartyPerMonth" xlink:label="brkh_RelatedPartyTransactionExpensesFromTransactionsWithRelatedPartyPerMonth" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_RelatedPartyTransactionExpensesFromTransactionsWithRelatedPartyPerMonth" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_GeneralAndAdministrativeExpense" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedLiabilitiesCurrent" xlink:label="us-gaap_AccruedLiabilitiesCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_AccruedLiabilitiesCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumLoansConvertibleIntoWarrants" xlink:label="brkh_MaximumLoansConvertibleIntoWarrants" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_MaximumLoansConvertibleIntoWarrants" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentConvertibleConversionPrice1" xlink:label="us-gaap_DebtInstrumentConvertibleConversionPrice1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_DebtInstrumentConvertibleConversionPrice1" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentFaceAmount" xlink:label="us-gaap_DebtInstrumentFaceAmount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_DebtInstrumentFaceAmount" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NotesPayableCurrent" xlink:label="us-gaap_NotesPayableCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_NotesPayableCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LineOfCredit" xlink:label="us-gaap_LineOfCredit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_LineOfCredit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueFromSponsorCurrent" xlink:label="brkh_DueFromSponsorCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_DueFromSponsorCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DueToTrustAccountCurrent" xlink:label="brkh_DueToTrustAccountCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_RelatedPartyTransactionLineItems" xlink:to="brkh_DueToTrustAccountCurrent" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureCommitmentsAndContingenciesDetails" xlink:type="extended" xlink:title="40601 - Disclosure - COMMITMENTS AND CONTINGENCIES (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LossContingenciesTable" xlink:label="us-gaap_LossContingenciesTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TypeOfArrangementAxis" xlink:label="us-gaap_TypeOfArrangementAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_TypeOfArrangementAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_TypeOfArrangementAxis" xlink:to="us-gaap_ArrangementsAndNonarrangementTransactionsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NonRedemptionAgreementsMember" xlink:label="brkh_NonRedemptionAgreementsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="brkh_NonRedemptionAgreementsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionAxis" xlink:label="us-gaap_RelatedPartyTransactionAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_RelatedPartyTransactionAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionDomain" xlink:label="us-gaap_RelatedPartyTransactionDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionAxis" xlink:to="us-gaap_RelatedPartyTransactionDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_FounderSharesMember" xlink:label="brkh_FounderSharesMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_FounderSharesMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_LockUpAgreementMember" xlink:label="brkh_LockUpAgreementMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyTransactionDomain" xlink:to="brkh_LockUpAgreementMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MergerAgreementMember" xlink:label="brkh_MergerAgreementMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="brkh_MergerAgreementMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SponsorMember" xlink:label="brkh_SponsorMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="brkh_SponsorMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="4" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_SubsequentEventTypeAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeAxis" xlink:label="us-gaap_MeasurementInputTypeAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="5" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_MeasurementInputTypeAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeDomain" xlink:label="us-gaap_MeasurementInputTypeDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_MeasurementInputTypeAxis" xlink:to="us-gaap_MeasurementInputTypeDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ProbabilityOfSuccessfulBusinessCombinationMember" xlink:label="brkh_ProbabilityOfSuccessfulBusinessCombinationMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_MeasurementInputTypeDomain" xlink:to="brkh_ProbabilityOfSuccessfulBusinessCombinationMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputPriceVolatilityMember" xlink:label="us-gaap_MeasurementInputPriceVolatilityMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_MeasurementInputTypeDomain" xlink:to="us-gaap_MeasurementInputPriceVolatilityMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputExercisePriceMember" xlink:label="us-gaap_MeasurementInputExercisePriceMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_MeasurementInputTypeDomain" xlink:to="us-gaap_MeasurementInputExercisePriceMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="6" xlink:from="us-gaap_LossContingenciesTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_CounterpartyNameAxis" xlink:label="srt_CounterpartyNameAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="7" xlink:from="us-gaap_LossContingenciesTable" xlink:to="srt_CounterpartyNameAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RepurchaseAgreementCounterpartyNameDomain" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="srt_CounterpartyNameAxis" xlink:to="srt_RepurchaseAgreementCounterpartyNameDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_EfHuttonMember" xlink:label="brkh_EfHuttonMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="brkh_EfHuttonMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LossContingenciesLineItems" xlink:label="us-gaap_LossContingenciesLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_LossContingenciesTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumNumberOfDemandsForRegistrationOfSecurities" xlink:label="brkh_MaximumNumberOfDemandsForRegistrationOfSecurities" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_MaximumNumberOfDemandsForRegistrationOfSecurities" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_UnderwritingCashDiscountPercentagePerUnit" xlink:label="brkh_UnderwritingCashDiscountPercentagePerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_UnderwritingCashDiscountPercentagePerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SaleOfStockUnderwritingFees" xlink:label="brkh_SaleOfStockUnderwritingFees" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_SaleOfStockUnderwritingFees" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DeferredUnderwritingDiscountPercentagePerUnit" xlink:label="brkh_DeferredUnderwritingDiscountPercentagePerUnit" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_DeferredUnderwritingDiscountPercentagePerUnit" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DeferredOfferingCostsNoncurrent" xlink:label="brkh_DeferredOfferingCostsNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_DeferredOfferingCostsNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodValueNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharesIssuedPricePerShare" xlink:label="us-gaap_SharesIssuedPricePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_SharesIssuedPricePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" xlink:label="brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_MaximumNumberOfSharesTransferredInExchangeForNotForRedemptionOfShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_EquityFairValueStockholderNonRedemptionAgreement" xlink:label="brkh_EquityFairValueStockholderNonRedemptionAgreement" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_EquityFairValueStockholderNonRedemptionAgreement" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AgreementFairValuePerShare" xlink:label="brkh_AgreementFairValuePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_AgreementFairValuePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:label="us-gaap_EquitySecuritiesFvNiMeasurementInput" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_EquitySecuritiesFvNiMeasurementInput" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodShares" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodValue" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="15" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SalesAndExciseTaxPayableCurrent" xlink:label="us-gaap_SalesAndExciseTaxPayableCurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="16" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="us-gaap_SalesAndExciseTaxPayableCurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PercentageOfSharesRedeemed" xlink:label="brkh_PercentageOfSharesRedeemed" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="17" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_PercentageOfSharesRedeemed" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="18" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PercentageOfBeneficialOwnershipHeld" xlink:label="brkh_PercentageOfBeneficialOwnershipHeld" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="19" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_PercentageOfBeneficialOwnershipHeld" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" xlink:label="brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="20" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_TransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombinationStockPriceTrigger" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="21" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_ThresholdTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" xlink:label="brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="22" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_ThresholdConsecutiveTradingDaysForTransferAssignOrSaleOfSharesOrWarrantsAfterCompletionOfInitialBusinessCombinations" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" xlink:label="brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="23" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_ThresholdPeriodAfterBusinessCombinationInWhichSpecifiedTradingDaysWithinAnySpecifiedTradingDayPeriodCommences" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_NumberOfSharesAgreedToForfeitBySponsorToBeEffectiveImmediatelyPriorToBusinessCombination" xlink:label="brkh_NumberOfSharesAgreedToForfeitBySponsorToBeEffectiveImmediatelyPriorToBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="24" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_NumberOfSharesAgreedToForfeitBySponsorToBeEffectiveImmediatelyPriorToBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_AggregateReserveSizedUnderEquityIncentivePlanAndEsppPercentage" xlink:label="brkh_AggregateReserveSizedUnderEquityIncentivePlanAndEsppPercentage" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="25" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_AggregateReserveSizedUnderEquityIncentivePlanAndEsppPercentage" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_EvergreenPercentageForEquityIncentivePlan" xlink:label="brkh_EvergreenPercentageForEquityIncentivePlan" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="26" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_EvergreenPercentageForEquityIncentivePlan" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_BasePurchasePrice" xlink:label="brkh_BasePurchasePrice" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="27" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_BasePurchasePrice" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SharesConsideredForCalculatingProportionateShares" xlink:label="brkh_SharesConsideredForCalculatingProportionateShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="28" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_SharesConsideredForCalculatingProportionateShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CashPaymentAgreedInLieuOfFullDeferredUnderwritingCommission" xlink:label="brkh_CashPaymentAgreedInLieuOfFullDeferredUnderwritingCommission" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="29" xlink:from="us-gaap_LossContingenciesLineItems" xlink:to="brkh_CashPaymentAgreedInLieuOfFullDeferredUnderwritingCommission" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureStockholdersDeficitCommonStockSharesDetails" xlink:type="extended" xlink:title="40702 - Disclosure - STOCKHOLDERS' DEFICIT - Common Stock Shares (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfStockByClassTable" xlink:label="us-gaap_ScheduleOfStockByClassTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_ScheduleOfStockByClassTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassAMember" xlink:label="us-gaap_CommonClassAMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassAMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaSubjectToRedemptionMember" xlink:label="brkh_CommonClassaSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_CommonClassAMember" xlink:to="brkh_CommonClassaSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonClassaNotSubjectToRedemptionMember" xlink:label="brkh_CommonClassaNotSubjectToRedemptionMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="brkh_CommonClassaSubjectToRedemptionMember" xlink:to="brkh_CommonClassaNotSubjectToRedemptionMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockLineItems" xlink:label="us-gaap_ClassOfStockLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_ScheduleOfStockByClassTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesAuthorized" xlink:label="us-gaap_CommonStockSharesAuthorized" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_CommonStockSharesAuthorized" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockParOrStatedValuePerShare" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_CommonStockParOrStatedValuePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_CommonStockNumberOfVotesPerShare" xlink:label="brkh_CommonStockNumberOfVotesPerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="brkh_CommonStockNumberOfVotesPerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" xlink:label="brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="brkh_StockIssuedDuringPeriodSharesConversionFromOneClassOfStockToAnother" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesIssued" xlink:label="us-gaap_CommonStockSharesIssued" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_CommonStockSharesIssued" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesOutstanding" xlink:label="us-gaap_CommonStockSharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_CommonStockSharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesOutstanding" xlink:label="us-gaap_TemporaryEquitySharesOutstanding" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_TemporaryEquitySharesOutstanding" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_StockIssuedDuringPeriodSharesNewIssues" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodShares" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodShares" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_TemporaryEquityStockRedeemedDuringPeriodValue" xlink:label="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="brkh_TemporaryEquityStockRedeemedDuringPeriodValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityRedemptionPricePerShare" xlink:label="us-gaap_TemporaryEquityRedemptionPricePerShare" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_TemporaryEquityRedemptionPricePerShare" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsHeldInTrustNoncurrent" xlink:label="us-gaap_AssetsHeldInTrustNoncurrent" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="us-gaap_AssetsHeldInTrustNoncurrent" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ConvertibleStockConversionRatio" xlink:label="brkh_ConvertibleStockConversionRatio" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="us-gaap_ClassOfStockLineItems" xlink:to="brkh_ConvertibleStockConversionRatio" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" xlink:label="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="brkh_ConvertibleStockConversionRatio" xlink:to="us-gaap_StockholdersEquityNoteStockSplitConversionRatio1" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureStockholdersDeficitWarrantsDetails" xlink:type="extended" xlink:title="40703 - Disclosure - STOCKHOLDERS' DEFICIT - Warrants (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightTable" xlink:label="us-gaap_ClassOfWarrantOrRightTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis" xlink:label="us-gaap_ClassOfWarrantOrRightAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightTable" xlink:to="us-gaap_ClassOfWarrantOrRightAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain" xlink:label="us-gaap_ClassOfWarrantOrRightDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightAxis" xlink:to="us-gaap_ClassOfWarrantOrRightDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantMember" xlink:label="us-gaap_WarrantMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightDomain" xlink:to="us-gaap_WarrantMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PublicWarrantsMember" xlink:label="brkh_PublicWarrantsMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_WarrantMember" xlink:to="brkh_PublicWarrantsMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_StatementScenarioAxis" xlink:label="srt_StatementScenarioAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_ClassOfWarrantOrRightTable" xlink:to="srt_StatementScenarioAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_ScenarioUnspecifiedDomain" xlink:label="srt_ScenarioUnspecifiedDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="srt_StatementScenarioAxis" xlink:to="srt_ScenarioUnspecifiedDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_RedemptionOfWarrantsWhenPricePerShareOfClassCommonStockEqualsOrExceeds18.00Member" xlink:label="brkh_RedemptionOfWarrantsWhenPricePerShareOfClassCommonStockEqualsOrExceeds18.00Member" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="srt_ScenarioUnspecifiedDomain" xlink:to="brkh_RedemptionOfWarrantsWhenPricePerShareOfClassCommonStockEqualsOrExceeds18.00Member" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis" xlink:label="us-gaap_StatementClassOfStockAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_ClassOfWarrantOrRightTable" xlink:to="us-gaap_StatementClassOfStockAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain" xlink:label="us-gaap_ClassOfStockDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_StatementClassOfStockAxis" xlink:to="us-gaap_ClassOfStockDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonClassBMember" xlink:label="us-gaap_CommonClassBMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_ClassOfStockDomain" xlink:to="us-gaap_CommonClassBMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightLineItems" xlink:label="us-gaap_ClassOfWarrantOrRightLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SharePriceTriggerUsedToMeasureDilutionOfWarrants" xlink:label="brkh_SharePriceTriggerUsedToMeasureDilutionOfWarrants" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_SharePriceTriggerUsedToMeasureDilutionOfWarrants" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantsAndRightsOutstandingTerm" xlink:label="us-gaap_WarrantsAndRightsOutstandingTerm" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="4" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="us-gaap_WarrantsAndRightsOutstandingTerm" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_WarrantsAndRightsOutstandingExercisableTermAfterBusinessCombination" xlink:label="brkh_WarrantsAndRightsOutstandingExercisableTermAfterBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="5" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_WarrantsAndRightsOutstandingExercisableTermAfterBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_WarrantsAndRightsOutstandingExercisableTermFromClosingOfInitialPublicOffering" xlink:label="brkh_WarrantsAndRightsOutstandingExercisableTermFromClosingOfInitialPublicOffering" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="6" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_WarrantsAndRightsOutstandingExercisableTermFromClosingOfInitialPublicOffering" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodForRegistrationStatementToBeEffectiveAfterWhichWarrantsCanBeExercisedOnCashlessBasis" xlink:label="brkh_ThresholdPeriodForRegistrationStatementToBeEffectiveAfterWhichWarrantsCanBeExercisedOnCashlessBasis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="7" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ThresholdPeriodForRegistrationStatementToBeEffectiveAfterWhichWarrantsCanBeExercisedOnCashlessBasis" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightRedemptionPriceOfWarrantsOrRights" xlink:label="brkh_ClassOfWarrantOrRightRedemptionPriceOfWarrantsOrRights" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="8" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightRedemptionPriceOfWarrantsOrRights" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_RedemptionPeriod" xlink:label="brkh_RedemptionPeriod" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="9" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_RedemptionPeriod" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsStockPriceTrigger" xlink:label="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsStockPriceTrigger" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="10" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsStockPriceTrigger" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightAdjustmentOfRedemptionPriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice2" xlink:label="brkh_ClassOfWarrantOrRightAdjustmentOfRedemptionPriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice2" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="11" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightAdjustmentOfRedemptionPriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice2" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdTradingDays" xlink:label="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdTradingDays" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="12" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdTradingDays" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdConsecutiveTradingDays" xlink:label="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdConsecutiveTradingDays" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="13" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightRedemptionOfWarrantsOrRightsThresholdConsecutiveTradingDays" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdNumberOfBusinessDaysBeforeSendingNoticeOfRedemptionToWarrantHolders" xlink:label="brkh_ThresholdNumberOfBusinessDaysBeforeSendingNoticeOfRedemptionToWarrantHolders" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="14" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ThresholdNumberOfBusinessDaysBeforeSendingNoticeOfRedemptionToWarrantHolders" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_PercentageOfGrossProceedsOnTotalEquityProceeds" xlink:label="brkh_PercentageOfGrossProceedsOnTotalEquityProceeds" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="15" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_PercentageOfGrossProceedsOnTotalEquityProceeds" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdTradingDaysForCalculatingMarketValue" xlink:label="brkh_ThresholdTradingDaysForCalculatingMarketValue" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="16" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ThresholdTradingDaysForCalculatingMarketValue" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdIssuePriceForCapitalRaisingPurposesInConnectionWithClosingOfBusinessCombination" xlink:label="brkh_ThresholdIssuePriceForCapitalRaisingPurposesInConnectionWithClosingOfBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="17" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ThresholdIssuePriceForCapitalRaisingPurposesInConnectionWithClosingOfBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightAdjustmentOfExercisePriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice" xlink:label="brkh_ClassOfWarrantOrRightAdjustmentOfExercisePriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="18" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightAdjustmentOfExercisePriceOfWarrantsOrRightsPercentBasedOnMarketValueAndNewlyIssuedPrice" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" xlink:label="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="19" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ThresholdPeriodForNotToTransferAssignOrSellAnySharesOrWarrantsAfterCompletionOfInitialBusinessCombination" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_ClassOfWarrantOrRightMinimumThresholdWrittenNoticePeriodForRedemptionOfWarrants" xlink:label="brkh_ClassOfWarrantOrRightMinimumThresholdWrittenNoticePeriodForRedemptionOfWarrants" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="20" xlink:from="us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="brkh_ClassOfWarrantOrRightMinimumThresholdWrittenNoticePeriodForRedemptionOfWarrants" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureFairValueMeasurementsDetails" xlink:type="extended" xlink:title="40901 - Disclosure - FAIR VALUE MEASUREMENTS (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueByFairValueHierarchyLevelAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel1Member" xlink:label="us-gaap_FairValueInputsLevel1Member" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="us-gaap_FairValueInputsLevel1Member" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinancialInstrumentAxis" xlink:label="us-gaap_FinancialInstrumentAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FinancialInstrumentAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_FinancialInstrumentAxis" xlink:to="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_U.s.MoneyMarketFundHeldInTrustAccountMember" xlink:label="brkh_U.s.MoneyMarketFundHeldInTrustAccountMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:to="brkh_U.s.MoneyMarketFundHeldInTrustAccountMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByMeasurementFrequencyAxis" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="3" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="us-gaap_FairValueByMeasurementFrequencyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementFrequencyDomain" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_FairValueByMeasurementFrequencyAxis" xlink:to="us-gaap_FairValueMeasurementFrequencyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementsRecurringMember" xlink:label="us-gaap_FairValueMeasurementsRecurringMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_FairValueMeasurementFrequencyDomain" xlink:to="us-gaap_FairValueMeasurementsRecurringMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsFairValueDisclosureAbstract" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="us-gaap_AssetsFairValueDisclosureAbstract" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsFairValueDisclosure" xlink:label="us-gaap_AssetsFairValueDisclosure" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_AssetsFairValueDisclosureAbstract" xlink:to="us-gaap_AssetsFairValueDisclosure" priority="1" use="optional" />
  </definitionLink>
  <definitionLink xlink:role="http://burtechacquisitioncorp.com/role/DisclosureSubsequentEventsDetails" xlink:type="extended" xlink:title="41001 - Disclosure - SUBSEQUENT EVENTS (Details)" xmlns="http://www.xbrl.org/2003/linkbase">
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTable" xlink:label="us-gaap_SubsequentEventTable" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis" xlink:label="us-gaap_SubsequentEventTypeAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="1" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_SubsequentEventTypeAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeDomain" xlink:label="us-gaap_SubsequentEventTypeDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_SubsequentEventTypeAxis" xlink:to="us-gaap_SubsequentEventTypeDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventMember" xlink:label="us-gaap_SubsequentEventMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_SubsequentEventTypeDomain" xlink:to="us-gaap_SubsequentEventMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/hypercube-dimension" order="2" xlink:from="us-gaap_SubsequentEventTable" xlink:to="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyDomain" xlink:label="us-gaap_RelatedPartyDomain" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/dimension-domain" order="1" xlink:from="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="us-gaap_RelatedPartyDomain" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RelatedPartyMember" xlink:label="us-gaap_RelatedPartyMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyDomain" xlink:to="us-gaap_RelatedPartyMember" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SponsorMember" xlink:label="brkh_SponsorMember" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="1" xlink:from="us-gaap_RelatedPartyMember" xlink:to="brkh_SponsorMember" use="optional" />
    <loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventLineItems" xlink:label="us-gaap_SubsequentEventLineItems" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/all" order="1" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="us-gaap_SubsequentEventTable" use="optional" xbrldt:contextElement="segment" xbrldt:closed="true" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_DepositInTrustAccount" xlink:label="brkh_DepositInTrustAccount" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="2" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="brkh_DepositInTrustAccount" priority="1" use="optional" />
    <loc xlink:type="locator" xlink:href="brkh-20231231.xsd#brkh_SharesConsideredForCalculatingProportionateShares" xlink:label="brkh_SharesConsideredForCalculatingProportionateShares" />
    <definitionArc xlink:type="arc" xlink:arcrole="http://xbrl.org/int/dim/arcrole/domain-member" order="3" xlink:from="us-gaap_SubsequentEventLineItems" xlink:to="brkh_SharesConsideredForCalculatingProportionateShares" priority="1" use="optional" />
  </definitionLink>
</link:linkbase>
