Linear Algebra (Larry Smith).pdf

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1、UndergraduateTextsinMathematicsEditorsF.W.GehringP.R.HalmosAdvisoryBoardC.DePrimaI.HersteinJ.KieferLarrySmithLinearAlgebraSpringer-VerlagNewYorkHeidelbergBerlinLarrySmithMathematischesInstitutorIndianaUniversityUniversitatG6ttingenDepartmentofMathematicsD3400G6ttingenBloomington,Indiana4

2、7401WestGermanyUSAEditorialBoardF.W.GehringP.R.HalmosUniversityofMichiganUniversityofCaliforniaDepartmentofMathematicsDepartmentofMathematicsAnnArbor,Michigan48104SantaBarbara.California93106USAUSAAMSSubjectClassifications:15-01LibraryofCongressCataloginginPublicationDataSmith,Larry.Line

3、aralgebra.(Undergraduatetextsinmathematics)Includesindex.1.Algebras,Linear.I.Title.QA184.S63512'.577-1209Allrightsreserved.NopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenpermissionfromSpringer-Verlag.©1978bySpringer-Verlag,NewYorkInc.Softcoverreprintofthehardcover1sted

4、ition197898765432IISBN-13:978-1-4615-9997-5e-ISBN-13:978-1-4615-9995-1DOl:10.1007/978-1-4615-9995-1DedicatedtoMi-SoowithoutwhomthisbookandmanyotherthingscouldnotexistPrefaceThistextiswrittenforacourseinlinearalgebraatthe(U.S.)sophomoreundergraduatelevel,preferablydirectlyfollowingaone-va

5、riablecalculuscourse,sothatlinearalgebracanbeusedinacourseonmultidimensionalcalculus.Realizingthatstudentsatthislevelhavehadlittlecontactwithcomplexnumbersorabstractmathematicsthebookdealsalmostexclusivelywithrealfinite-dimensionalvectorspacesinasettingandformulationthatpermitseasygenera

6、lizationtoabstractvectorspaces.Theparallelcomplextheoryisdevelopedintheexercises.Thebookhasasagoaltheprincipalaxistheoremforrealsymmetrictransformations,andamoreorlessdirectpathisfollowed.Asaconsequencetherearemanysubjectsthatarenotdeveloped,andthisisintentional.Howeverawideselectionofex

7、amplesofvectorspacesandlineartrans•formationsisdeveloped,inthehopethattheywillserveasatestinggroundforthetheory.Thebookismeantasanintroductiontolinearalgebraandthetheorydevelopedcontainstheessentialsforthisgoal.Studentswithaneedtolearnmorelinearalgebracandosoinacourseinab