文档介绍：The Linear Algebra a Beginning GraduateStudent Ought to KnowJonathan S. GolanThe Linear Algebraa Beginning GraduateStudent Oughtto KnowThird EditionProf. Jonathan S. GolanDept. of MathematicsUniversity of HaifaHaifaIsraelISBN 978-94-007-2635-2e-ISBN 978-94-007-2636-9DOI -94-007-2636-9Springer Dordrecht Heidelberg London New YorkLibrary of Congress Control Number: 2012933373Mathematics Subject Classi?cation (2010): 15-XX, 16-XX, 17-XX, 65F30?Springer Science+Business Media . 2004, 2007, 2012No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or byany means, electronic, mechanical, photocopying, micro?lming, recording or otherwise, without writtenpermission from the Publisher, with the exception of any material supplied speci?cally for the purposeof being entered and executed on puter system, for exclusive use by the purchaser of the we have made considerable efforts to contact all holders of copyright material contained in thisbook. We have failed to locate some of them. Should holders wish to contact the Publisher, we will makeevery effort e to some arrangement with on acid-free paperSpringer is part of Springer Science+Business Media ( the memory of Hemda, my wife of over 40years:And to my grandchildren: Shachar, Eitan,Sarel, Nachshon, Yarden, Itamar, Roni, andNaomiFor WhomIs This Book Written?Crow’s Law: Do not think what you want to think until you know what youought to algebra is a living, active branch of mathematical research which is centralto almost all other areas of mathematics and which has important applications in allbranches of the physical and social sciences and in engineering. However, in recentyears the content of linear algebra courses required plete an undergraduatedegree in mathematics—and even more so in other areas—at all but the most ded-icated universities, has been depleted to the extent that it falls far short of what isin fact needed for gradu