线性代数（第2版）（英文影印版）

Theaudacioustitleofthisbookdeservesanexplanation.Almostalllinearalgebrabooksusedeterminantstoprovethateverylinearoperatoronafinite-dimensionalcomplexvectorspacehasaneigenvalue.Determinantsaredifficult,nonintuitive,andoftendefinedwithoutmotivation.Toprovethetheoremaboutexistenceofeigenvaluesoncomplexvectorspaces,mostbooksmust.definedeterminants,provethatalinearmapisnotinvertibleffandonlyifitsdeterminantequalsO,andthendefinethecharacteristicpolynomial.Thistortuous(torturous?)pathgivesstudentslittlefeelingforwhyeigenvaluesmustexist.Incontrast,thesimpledeterminant-freeproofspresentedhereoffermoreinsight.Oncedeterminantshavebeenbanishedtotheendofthebook,anewrouteopenstothemaingoaloflinearalgebra--understandingthestructureoflinearoperators.