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1、AlgorithmsandCombinatoricsVolume20EditorialBoardR.L.Graham,LaJollaB.Korte,BonnL.Lovasz,Budapest´A.Wigderson,PrincetonG.M.Ziegler,BerlinKazuoMurotaMatricesandMatroidsforSystemsAnalysis13KazuoMurotaDepartmentofMathematicalInformaticsGraduateSchoolofInformationScienceandTechnologyUniversity
2、ofTokyoTokyo,113-8656Japanmurota@mist.i.u-tokyo.ac.jpISBN978-3-642-03993-5e-ISBN978-3-642-03994-2DOI10.1007/978-3-642-03994-2SpringerHeidelbergDordrechtLondonNewYorkLibraryofCongressControlNumber:2009937412cSpringer-VerlagBerlinHeidelberg2000,firstcorrectedsoftcoverprinting2010Thisworkis
3、subjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermitte
4、donlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,
5、evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesigndeblik,BerlinPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)PrefaceInterplaybetweenmatrixtheoryandmatroidth
6、eoryisthemainthemeofthisbook,whichoffersamatroid-theoreticapproachtolinearalgebraand,reciprocally,alinear-algebraicapproachtomatroidtheory.Thebookservesalsoasthefirstcomprehensivepresentationofthetheoryandapplicationofmixedmatricesandmixedpolynomialmatrices.Amatroidisanabstractmathematical
7、structurethatcapturescombi-natorialpropertiesofmatrices,andcombinatorialpropertiesofmatrices,inturn,canbestatedandanalyzedsuccessfullywiththeaidofmatroidthe-ory.Themostimportantresultinmatroidtheory,deepestinmathematicalcontentandmostusefulinapplication,istheintersectiont
