NowavailableinOpenAccess,thisbest-sellingtextbookforasecondcourseinlinearalgebraisaimedatundergraduatemathmajorsandgraduatestudents.Thefourtheditiongivesanexpandedtreatmentofthesingularvaluedecompositionanditsconsequences.Itincludesanewchapteronmultilinearalgebra,treatingbilinearforms,quadraticforms,tensorproducts,andanapproachtodeterminantsviaalternatingmultilinearforms.Thisneweditionalsoincreasestheuseoftheminimalpolynomialtoprovidecleanerproofsofmultipleresults.Also,over250newexerciseshavebeenadded.Thenovelapproachtakenherebanishesdeterminantstotheendofthebook.Thetextfocusesonthecentralgoaloflinearalgebra:understandingthestructureoflinearoperatorsonfinite-dimensionalvectorspaces.Theauthorhastakenunusualcaretomotivateconceptsandsimplifyproofs.Avarietyofinterestingexercisesineachchapterhelpsstudentsunderstandandmanipulatetheobjectsoflinearalgebra.Beautifulformattingcreatespageswithanunusuallystudent-friendlyappearanceinbothprintandelectronicversions.Noprerequisitesareassumedotherthantheusualdemandforsuitablemathematicalmaturity.Thetextstartsbydiscussingvectorspaces,linearindependence,span,basis,anddimension.Thebookthendealswithlinearmaps,eigenvalues,andeigenvectors.Inner-productspacesareintroduced,leadingtothefinite-dimensionalspectraltheoremanditsconsequences.Generalizedeigenvectorsarethenusedtoprovideinsightintothestructureofalinearoperator.Fromthereviewsofpreviouseditions:Altogether,thetextisadidacticmasterpiece.--zbMATHThedeterminant-freeproofsareelegantandintuitive.--AmericanMathematicalMonthlyThemostoriginallinearalgebrabooktoappearinyears,itcertainlybelongsineveryundergraduatelibrary--CHOICE
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