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1、ThispageintentionallyleftblankLINEARALGEBRAAGeometricApproachsecondeditionThispageintentionallyleftblankLINEARALGEBRAAGeometricApproachsecondeditionTheodoreShifrinMalcolmR.AdamsUniversityofGeorgiaW.H.FreemanandCompanyNewYorkPublisher:RuthBaruthSeniorAcquisitionsEditor:TerriWardExecutiv
2、eMarketingManager:JenniferSomervilleAssociateEditor:KatrinaWilhelmEditorialAssistant:LaurenKimmichPhotoEditor:BiancaMoscatelliCoverandTextDesigner:BlakeLoganProjectEditors:LeighRenhardandTechsetters,Inc.Illustrations:Techsetters,Inc.SeniorIllustrationCoordinator:BillPageProductionManag
3、er:EllenCashComposition:Techsetters,Inc.PrintingandBinding:RRDonnelleyLibraryofCongressControlNumber:2010921838ISBN-13:978-1-4292-1521-3ISBN-10:1-4292-1521-6?2011,2002byW.H.FreemanandCompanyAllrightsreservedPrintedintheUnitedStatesofAmericaFirstprintingW.H.FreemanandCompany41MadisonAve
4、nueNewYork,NY10010Houndmills,BasingstokeRG216XS,Englandwww.whfreeman.comCONTENTSPrefaceviiForewordtotheInstructorxiiiForewordtotheStudentxviiChapter1VectorsandMatrices11.Vectors12.DotProduct183.HyperplanesinRn284.SystemsofLinearEquationsandGaussianElimination365.TheTheoryofLinearSystem
5、s536.SomeApplications64Chapter2MatrixAlgebra811.MatrixOperations812.LinearTransformations:AnIntroduction913.InverseMatrices1024.ElementaryMatrices:RowsGetEqualTime1105.TheTranspose119Chapter3VectorSpaces1271.SubspacesofRn1272.TheFourFundamentalSubspaces1363.LinearIndependenceandBasis14
6、34.DimensionandItsConsequences1575.AGraphicExample1706.AbstractVectorSpaces176vviContentsChapter4ProjectionsandLinearTransformations1911.InconsistentSystemsandProjection1912.OrthogonalBases2003.TheMatrixofaLinearTransformationandtheChange-of-BasisFormula2084.LinearTransformationsonAbst
7、ractVectorSpaces224Chapter5Determinants2391.PropertiesofDeterminants2392.CofactorsandCramer’sRule2453.SignedAreainR2andSignedVolumeinR3255Chapter6EigenvaluesandEigenvectors2611.TheCharacteristicPolynomial2612.Diagonalizability2703.Applications2774.TheSpectralTheorem286Chapter7Further
