资源描述:
《Schaum's Outlines - Linear Algebra, 3rd Edition》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、Lipschutz−Lipson:SchaumsFrontMatterPreface©TheMcGraw−HillOutlineofTheoryandCompanies,2004ProblemsofLinearAlgebra,3/ePREFACELinearalgebrahasinrecentyearsbecomeanessentialpartofthemathemticalbackgroundrequiredbymathematiciansandmathematicsteachers,engineers,computerscientists,physicists,eco
2、nomists,andstatisti-cians,amongothers.Thisrequirementre¯ectstheimportanceandwideapplicationsofthesubjectmatter.Thisbookisdesignedforuseasatextbookforaformalcourseinlinearalgebraorasasupplementtoallcurrentstandardtexts.Itaimstopresentanintroductiontolinearalgebrawhichwillbefoundhelpfultoal
3、lreadersregardlessoftheir®eldsofspeci®cation.Morematerialhasbeenincludedthancanbecoveredinmost®rstcourses.Thishasbeendonetomakethebookmore¯exible,toprovideausefulbookofreference,andtostimulatefurtherinterestinthesubject.Eachchapterbeginswithclearstatementsofpertinentde®nitions,principlesa
4、ndtheoremstogetherwithillustrativeandotherdescriptivematerial.Thisisfollowedbygradedsetsofsolvedandsupplementaryproblems.Thesolvedproblemsservetoillustrateandamplifythetheory,andtoprovidetherepetitionofbasicprinciplessovitaltoeffectivelearning.Numerousproofs,especiallythoseofallessentialt
5、heorems,areincludedamongthesolvedproblems.Thesupplementaryproblemsserveasacompletereviewofthematerialofeachchapter.The®rstthreechapterstreatvectorsinEuclideanspace,matrixalgebra,andsystemsoflinearequations.Thesechaptersprovidethemotivationandbasiccomputationaltoolsfortheabstractinvestigat
6、ionofvectorspacesandlinearmappingswhichfollow.Afterchaptersoninnerproductspacesandorthogonalityandondeterminants,thereisadetaileddiscussionofeigenvaluesandeigenvectorsgivingconditionsforrepresentingalinearoperatorbyadiagonalmatrix.Thisnaturallyleadstothestudyofvariouscanonicalforms,speci®
7、cally,thetriangular,Jordan,andrationalcanonicalforms.LaterchapterscoverlinearfunctionsandthedualspaceV*,andbilinear,quadraticandHermitianforms.Thelastchaptertreatslinearoperatorsoninnerproductspaces.Forcompleteness,thereisanappendixonpolynomialsovera®eld.Themainchan