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A First Course in Linear Algebra(Robert A.Beezer).pdf

A First Course in Linear Algebr…

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简介:本文档为《A First Course in Linear Algebra(Robert A.Beezer)pdf》,可适用于高等教育领域,主题内容包含AFirstCourseinLinearAlgebraAFirstCourseinLinearAlgebrabyRobertABeezerDepar符等。

AFirstCourseinLinearAlgebraAFirstCourseinLinearAlgebrabyRobertABeezerDepartmentofMathematicsandComputerScienceUniversityofPugetSoundVersionRobertABeezerisaProfessorofMathematicsattheUniversityofPugetSound,wherehehasbeenonthefacultysinceHereceivedaBSinMathematics(withanEmphasisinComputerScience)fromtheUniversityofSantaClarain,aMSinStatisticsfromtheUniversityofIllinoisatUrbanaChampaigninandaPhDinMathematicsfromtheUniversityofIllinoisatUrbanaChampaigninHeteachescalculus,linearalgebraandabstractalgebraregularly,whilehisresearchinterestsincludetheapplicationsoflinearalgebratographtheoryHisprofessionalwebsiteisathttp:buzzardupseduEditionVersionMarch,PublisherRobertABeezerDepartmentofMathematicsandComputerScienceUniversityofPugetSoundNorthWarnerTacoma,WashingtonUSAcbyRobertABeezerPermissionisgrantedtocopy,distributeandormodifythisdocumentunderthetermsoftheGNUFreeDocumentationLicense,VersionoranylaterversionpublishedbytheFreeSoftwareFoundationwiththeInvariantSectionsbeing“Preface”,noFrontCoverTexts,andnoBackCoverTextsAcopyofthelicenseisincludedintheappendixentitled“GNUFreeDocumentationLicense”Themostrecentversionofthisworkcanalwaysbefoundathttp:linearupseduTomywife,PatContentsTableofContentsviContributorsviiDefinitionsviiiTheoremsixNotationxExamplesxiPrefacexiiAcknowledgementsxviiPartCCoreChapterSLESystemsofLinearEquationsWILAWhatisLinearAlgebraLA“Linear”“Algebra”AAAnApplicationREADReadingQuestionsEXCExercisesSOLSolutionsSSLESolvingSystemsofLinearEquationsSLESystemsofLinearEquationsPSSPossibilitiesforSolutionSetsESEOEquivalentSystemsandEquationOperationsREADReadingQuestionsEXCExercisesSOLSolutionsRREFReducedRowEchelonFormMVNSEMatrixandVectorNotationforSystemsofEquationsRORowOperationsRREFReducedRowEchelonFormREADReadingQuestionsEXCExercisesSOLSolutionsTSSTypesofSolutionSetsCSConsistentSystemsFVFreeVariablesREADReadingQuestionsEXCExercisesviCONTENTSviiSOLSolutionsHSEHomogeneousSystemsofEquationsSHSSolutionsofHomogeneousSystemsNSMSpaceofaMatrixREADReadingQuestionsEXCExercisesSOLSolutionsNMNonsingularMatricesNMNonsingularMatricesNSNMSpaceofaNonsingularMatrixREADReadingQuestionsEXCExercisesSOLSolutionsChapterVVectorsVOVectorOperationsVEASMVectorEquality,Addition,ScalarMultiplicationVSPVectorSpacePropertiesREADReadingQuestionsEXCExercisesSOLSolutionsLCLinearCombinationsLCLinearCombinationsVFSSVectorFormofSolutionSetsPSHSParticularSolutions,HomogeneousSolutionsURREFUniquenessofReducedRowEchelonFormREADReadingQuestionsEXCExercisesSOLSolutionsSSSpanningSetsSSVSpanofaSetofVectorsSSNSSpanningSetsofSpacesREADReadingQuestionsEXCExercisesSOLSolutionsLILinearIndependenceLISVLinearlyIndependentSetsofVectorsLINMLinearIndependenceandNonsingularMatricesNSSLISpaces,Spans,LinearIndependenceREADReadingQuestionsEXCExercisesSOLSolutionsLDSLinearDependenceandSpansLDSSLinearlyDependentSetsandSpansCOVCastingOutVectorsREADReadingQuestionsEXCExercisesSOLSolutionsOOrthogonalityCAVComplexArithmeticandVectorsIPInnerproductsNNormOVOrthogonalVectorsGSPGramSchmidtProcedureVersionCONTENTSviiiREADReadingQuestionsEXCExercisesChapterMMatricesMOMatrixOperationsMEASMMatrixEquality,Addition,ScalarMultiplicationVSPVectorSpacePropertiesTSMTransposesandSymmetricMatricesMCCMatricesandComplexConjugationAMAdjointofaMatrixREADReadingQuestionsEXCExercisesSOLSolutionsMMMatrixMultiplicationMVPMatrixVectorProductMMMatrixMultiplicationMMEEMatrixMultiplication,EntrybyEntryPMMPropertiesofMatrixMultiplicationHMHermitianMatricesREADReadingQuestionsEXCExercisesSOLSolutionsMISLEMatrixInversesandSystemsofLinearEquationsIMInverseofaMatrixCIMComputingtheInverseofaMatrixPMIPropertiesofMatrixInversesREADReadingQuestionsEXCExercisesSOLSolutionsMINMMatrixInversesandNonsingularMatricesNMINonsingularMatricesareInvertibleUMUnitaryMatricesREADReadingQuestionsEXCExercisesSOLSolutionsCRSColumnandRowSpacesCSSEColumnSpacesandSystemsofEquationsCSSOCColumnSpaceSpannedbyOriginalColumnsCSNMColumnSpaceofaNonsingularMatrixRSMRowSpaceofaMatrixREADReadingQuestionsEXCExercisesSOLSolutionsFSFourSubsetsLNSLeftSpaceCRSComputingColumnSpacesEEFExtendedechelonformFSFourSubsetsREADReadingQuestionsEXCExercisesSOLSolutionsChapterVSVectorSpacesVSVectorSpacesVersionCONTENTSixVSVectorSpacesEVSExamplesofVectorSpacesVSPVectorSpacePropertiesRDRecyclingDefinitionsREADReadingQuestionsEXCExercisesSOLSolutionsSSubspacesTSTestingSubspacesTSSTheSpanofaSetSCSubspaceConstructionsREADReadingQuestionsEXCExercisesSOLSolutionsLISSLinearIndependenceandSpanningSetsLILinearIndependenceSSSpanningSetsVRVectorRepresentationREADReadingQuestionsEXCExercisesSOLSolutionsBBasesBBasesBSCVBasesforSpansofColumnVectorsBNMBasesandNonsingularMatricesOBCOrthonormalBasesandCoordinatesREADReadingQuestionsEXCExercisesSOLSolutionsDDimensionDDimensionDVSDimensionofVectorSpacesRNMRankandityofaMatrixRNNMRankandityofaNonsingularMatrixREADReadingQuestionsEXCExercisesSOLSolutionsPDPropertiesofDimensionGTGoldilocks’TheoremRTRanksandTransposesDFSDimensionofFourSubspacesDSDirectSumsREADReadingQuestionsEXCExercisesSOLSolutionsChapterDDeterminantsDMDeterminantofaMatrixEMElementaryMatricesDDDefinitionoftheDeterminantCDComputingDeterminantsREADReadingQuestionsEXCExercisesSOLSolutionsVersionCONTENTSxPDMPropertiesofDeterminantsofMatricesDRODeterminantsandRowOperationsDROEMDeterminants,RowOperations,ElementaryMatricesDNMMMDeterminants,NonsingularMatrices,MatrixMultiplicationREADReadingQuestionsEXCExercisesSOLSolutionsChapterEEigenvaluesEEEigenvaluesandEigenvectorsEEMEigenvaluesandEigenvectorsofaMatrixPMPolynomialsandMatricesEEEExistenceofEigenvaluesandEigenvectorsCEEComputingEigenvaluesandEigenvectorsECEEExamplesofComputingEigenvaluesandEigenvectorsREADReadingQuestionsEXCExercisesSOLSolutionsPEEPropertiesofEigenvaluesandEigenvectorsMEMultiplicitiesofEigenvaluesEHMEigenvaluesofHermitianMatricesREADReadingQuestionsEXC

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