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1、JordanCanonicalFormTheoryandPracticeSynthesisLecturesonMathematicsandStatisticsEditorStevenG.Krantz,WashingtonUniversity,St.LouisJordanCanonicalForm:TheoryandPracticeStevenH.Weintraub2009TheGeometryofWalkerManifoldsMiguelBrozos-Vázquez,EduardoGarcía-Río,PeterGilkey,
2、StanaNikcevic,RámonVázquez-Lorenzo2009AnIntroductiontoMultivariableMathematicsLeonSimon2008JordanCanonicalForm:ApplicationtoDifferentialEquationsStevenH.Weintraub2008StatisticsisEasy!DennisShasha,MandaWilson2008AGyrovectorSpaceApproachtoHyperbolicGeometryAbrahamAlbe
3、rtUngar2008Copyright©2009byMorgan&ClaypoolAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeanselectronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotationsinprintedreviews,withouttheprior
4、permissionofthepublisher.JordanCanonicalForm:TheoryandPracticeStevenH.Weintraubwww.morganclaypool.comISBN:9781608452507paperbackISBN:9781608452514ebookDOI10.2200/S00218ED1V01Y200908MAS006APublicationintheMorgan&ClaypoolPublishersseriesSYNTHESISLECTURESONMATHEMATICSA
5、NDSTATISTICSLecture#6SeriesEditor:StevenG.Krantz,WashingtonUniversity,St.LouisSeriesISSNSynthesisLecturesonMathematicsandStatisticsPrint1938-1743Electronic1938-1751JordanCanonicalFormTheoryandPracticeStevenH.WeintraubLehighUniversitySYNTHESISLECTURESONMATHEMATICSAND
6、STATISTICS#6MMorgan&cLaypoolpublishers&CABSTRACTJordanCanonicalForm(JCF)isoneofthemostimportant,anduseful,conceptsinlinearalgebra.TheJCFofalineartransformation,orofamatrix,encodesallofthestructuralinformationaboutthatlineartransformation,ormatrix.Thisbookisacarefuld
7、evelopmentofJCF.Afterbeginningwithbackgroundmaterial,weintroduceJordanCanonicalFormandrelatednotions:eigenvalues,(generalized)eigenvectors,andthecharacteristicandminimumpolynomials.Wedecidetheques-tionofdiagonalizability,andprovetheCayleyHamiltontheorem.Thenwepresen
8、tacarefulandcompleteproofofthefundamentaltheorem:LetVbeafinite-dimensionalvectorspaceoverthefieldofcomplexnumbersC,andletT:V−→Vbealineartran
