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1、ANINTRODUCTIONTOMatrices,SetsandGroupsforScienceStudentsG.STEPHENSONB.sc.,PH.D,DIeEmeritusReaderinMathematicsImperialCollegeofScienceandTechnologyUniversityofLondonDoverPublications,Inc.NewYorkCopynght©1965byG.StephensonAllnghtsreservedunderPanAmencanandInternatlonalCopynghtConve
2、ntions.PublishedinCanadabyGeneralPublishingCompany,Ltd,30LesmIlIRoad,DonMills,Toronto,OntanoPublishedintheUnitedKingdombyConstableandCompany,Ltd,10OrangeStreet,LondonWC2H7EGThisDoveredition,firstpublishedin1986,ISanunabndgedandslightlycorrectedrepublicatIOnoftherevisedfourthImpre
3、s•sIOn(1974)oftheworkfirstpublishedbytheLongmanGroupLtd,London,in1965.ManufacturedintheUnitedStatesofAmencaDoverPublications,Inc,31East2ndStreet,Mineola,NY11501LibraryofCongressCataloging-in-PublicationDataStephenson,G(Geoffrey),1927-Anintroductiontomatrices,setsandgroupsforscien
4、cestudents.ReprintOriginallypublishedLondonLongmanGroup,1974.Includesindex.1Matrices2.Settheory3Groups,TheoryofITitleQA188.s691986512.9'43485-29370ISBN0-486-65077-4TOJOHNANDLYNNCONTENTSPrefacexi1.Sets,MappingsandTransformations1.1Introduction.11.2Sets11.3Venndiagrams41.4Mappings5
5、1.5Lineartransformationsandmatrices.81.6Occurrenceandusesofmatrices121.7Operationswithsets141.8Setalgebra.191.9Someelementaryapplicationsofsettheory20Problems1232.MatrixAlgebra2.1Lawsofmatrixalgebra252.2Partitioningofmatrices282.3Somespecialtypesofmatrices31Problems2.403.TheInver
6、seandRelatedMatrices3.1Introduction.433.2Theadjointmatrix.443.3Theinversematrix.463.4Somepropertiesoftheinversematrix473.5Evaluationoftheinversematrixbypartitioning483.6Orthogonalmatricesandorthogonaltransformations513.7Unitarymatrices56Problems3.584.SystemsofLinearAlgebraicEquat
7、ions4.1Introduction.624.2Non-homogeneousequations624.3Homogeneousequations674.4Ill-conditionedequations68Problems4.69Contents5.EigenvaluesandEigenvectors5.1Introduction.735.2Eigenvaluesandeigenvectors745.3Somepropertiesofeigenvalues785.4Repeatedeigenvalues795.5Orthogonalpropertie
8、sofeigenvectors825.6Realsymmetricmatrice
