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1、LINEARALGEBRASecondEditionKENNETHHOFFMANProfessorofMathematicsMassachusettsInstituteofTechnologyRAYKUNZEProfessorofMathematicsUniversityofCalifornia,IrvinePRENTICE-HALL,INC.,EnglewoodCliffs,NewJersey@1971,1961byPrentice-Hall,Inc.EnglewoodCliffs,NewJerseyAll
2、rightsreserved.Nopartofthisbookmaybereproducedinanyformorbyanymeanswithoutpermissioninwritingfromthepublisher.PRENTICE-HALL~NTERNATXONAL,INC.,LondonPRENTICE-HALLOFAUSTRALIA,PTY.LTD.,SydneyPRENTICE-HALLOFCANADA,LTD.,TorontoPRENTICE-HALLOFINDIAPRIVATELIMITED,
3、NewDelhiPRENTICE-HALLOFJAPAN,INC.,TokyoCurrentprinting(lastdigit):109876LibraryofCongressCatalogCardNo.75142120PrintedintheUnitedStatesofAmericaPfreaceOuroriginalpurposeinwritingthisbookwastoprovideatextfortheunder-graduatelinearalgebracourseattheMassachuse
4、ttsInstituteofTechnology.Thiscoursewasdesignedformathematicsmajorsatthejuniorlevel,althoughthree-fourthsofthestudentsweredrawnfromotherscientificandtechnologicaldisciplinesandrangedfromfreshmenthroughgraduatestudents.ThisdescriptionoftheM.I.T.audienceforthe
5、textremainsgenerallyaccuratetoday.ThetenyearssincethefirsteditionhaveseentheproliferationoflinearalgebracoursesthroughoutthecountryandhaveaffordedoneoftheauthorstheopportunitytoteachthebasicmaterialtoavarietyofgroupsatBrandeisUniversity,WashingtonUniver-sit
6、y(St.Louis),andtheUniversityofCalifornia(Irvine).OurprincipalaiminrevisingLinearAlgebrahasbeentoincreasethevarietyofcourseswhichcaneasilybetaughtfromit.Ononehand,wehavestructuredthechapters,especiallythemoredifficultones,sothatthereareseveralnaturalstop-pin
7、gpointsalongtheway,allowingtheinstructorinaone-quarterorone-semestercoursetoexerciseaconsiderableamountofchoiceinthesubjectmatter.Ontheotherhand,wehaveincreasedtheamountofmaterialinthetext,sothatitcanbeusedforarathercomprehensiveone-yearcourseinlinearalgebr
8、aandevenasareferencebookformathematicians.Themajorchangeshavebeeninourtreatmentsofcanonicalformsandinnerproductspaces.InChapter6wenolongerbeginwiththegeneralspatialtheorywhichunderliesthetheoryofcanoni
