Thistextbookgivesadetailedandcomprehensivepresentationoflinearalgebrabasedonanaxiomatictreatmentoflinearspaces.Forthisfourtheditionsomenewmaterialhasbeenaddedtothetext，forinstance，theintrinsictreatmentoftheclassicaladjointofalineartransformationinChapterIV，aswellasthediscussionofquaternionsandtheclassificationofassociativedivisionalgebrasinChapterVII.ChaptersXIIandXIIIhavebeensubstantiallyrewrittenforthesakeofclarity，butthecontentsremainbasicallythesameasbefore.Finally，anumberofproblemscoveringnewtopics-e.g.complexstructures，Caylaynumbersandsymplecticspaces-havebeenadded....