E-Book Overview
This is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, while others are conceptual.
E-Book Content
Undergraduate Texts in Mathematics
Serge Lang
Introduction to Linear Algebra Second Edition
•
Springer
Undergraduate Texts In Mathematics Editors
s.
Axler
F. W. Gehring K. A. Ribet
Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo
Springer Books on Elementary Mathematics by Serge Lang
MATH! Encounters with High School Students 1985, ISBN 96129-1 The Beauty of Doing Mathematics 1985, ISBN 96149-6 Geometry: A High School Course (with G. Murrow), Second Edition 1988, ISBN 96654-4 Basic Mathematics 1988, ISBN 96787-7 A First Course in Calculus, Fifth Edition 1986, ISBN 96201-8 Calculus of Several Variables, Third Edition 1987, ISBN 96405-3 Introduction to Linear Algebra, Second Edition 1986, ISBN 96205-0 Linear Algebra, Third Edition 1987, ISBN 96412-6 Undergraduate Algebra, Second Edition 1990, ISBN 97279-X Undergraduate Analysis, Second Edition 1997, ISBN 94841-4 Complex Analysis, Fourth Edition 1999, ISBN 98592-1 Real and Functional Analysis, Third Edition 1993, ISBN 94001-4
Serge Lang
Introduction to Linear Algebra Second Edition With 66 Illustrations
Springer
Serge Lang Department of Mathematics Yale University New Haven, CT 06520 U.S.A.
Editorial Board S. Axler Department of Mathematics Michigan State University East Lansing, MI 48824 U.S.A.
F. W. Gehring Department of Mathematics University of Michigan Ann Arbor. MI 48019 U.S.A.
K.A. Ribet Department of Mathelnatics University of California at Berkeley Berkeley, CA 94720-3840 U.S.A.
Mathematics Subjects Classifications (2000): 15-01
Library of Congress Cataloging in Publication Data Lang, Serge, 1927Introduction to linear algebra. (Undergraduate texts in mathematics) Includes index. 1. Algebras, Linear. I. Title. II. Series. QA184.L37 1986 512'.5 85-14758 Printed on acid-free paper. The first edition of this book was published by Addison-Wesley Publishing Company, Inc., in 1970.
© 1970, 1986 by Springer-Verlag New York Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, New York 10010, U.S.A.), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
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Preface
This book is meant as a short text in linear algebra for a one-term course. Except for an occasional example or exercise the text is logically independent of calculus, and could be taught early. In practice, I expect it