linear algebra and multidimensional geometry - r. sharipov

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1、RUSSIANFEDERALCOMMITTEEFORHIGHEREDUCATIONBASHKIRSTATEUNIVERSITYSHARIPOVR.A.COURSEOFLINEARALGEBRAANDMULTIDIMENSIONALGEOMETRYTheTextbookUfa19962MSC97U20PACS01.30.PpUDC512.64SharipovR.A.CourseofLinearAlgebraandMultidimensionalGeom-etry:thetextbook/Publ.ofBashkir

2、StateUniversity

3、Ufa,1996.

4、pp.143.ISBN5-7477-0099-5.Thisbookiswrittenasatextbookforthecourseofmultidimensionalgeometryandlinearalgebra.AtMathematicalDepartmentofBashkirStateUniversitythiscourseistaughttotherstyearstudentsintheSpringsemester.Itisapartofthebasi

5、cmathematicaleducation.Therefore,thiscourseistaughtatPhysicalandMathematicalDepartmentsinallUniversitiesofRussia.InpreparingRussianeditionofthisbookIusedthecomputertypesettingonthebaseoftheAMS-TEXpackageandIusedtheCyrillicfontsofLh-familydistributedbytheCyrTU

6、GassociationofCyrillicTEXusers.EnglisheditionofthisbookisalsotypesetbymeansoftheAMS-TEXpackage.Referees:ComputationalMathematicsandCyberneticsgroupofUfaStateUniversityforAircraftandTechnology(UGATU);Prof.S.I.Pinchuk,ChelyabinskStateUniversityforTechnol-ogy(QG

7、TU)andIndianaUniversity.Contactstoauthor.Oce:MathematicsDepartment,BashkirStateUniversity,32Frunzestreet,450074Ufa,RussiaPhone:7-(3472)-23-67-18Fax:7-(3472)-23-67-74Home:5Rabochayastreet,450003Ufa,RussiaPhone:7-(917)-75-55-786E-mails:RSharipov@ic.bashedu.rur

8、-sharipov@mail.rurasharipov@lycos.comrasharipov@hotmail.comURL:http://www.geocities.com/r-sharipovISBN5-7477-0099-5cSharipovR.A.,1996cBashkirStateUniversity,1996EnglishtranslationcSharipovR.A.,2004CONTENTS.CONTENTS.............................................

9、...................................................3.PREFACE...................................................................................................5.CHAPTERI.LINEARVECTORSPACESANDLINEARMAPPINGS.........6.x1.Thesetsandmappings......................

10、....................................................6.x2.Linearvectorspaces............................................................................10.x3.Lineardependenceandlinearindep