Introduction to Linear Algebra / Edition 2by Serge Lang
Pub. Date: 03/01/1997
Publisher: Springer New York
to Linear Algebra Second Edition With 66 Illustrations i Springer Serge Lang Department of Mathematics Yale University New Haven, CT 06520 U.SA Editorial Board S. Axler F. W. Gehring Department of Mathematics Department of Mathematics Michigan State University U niversity of Michigan East Lansing, MI 48824 Ann Arbor, MI 48019 U.SA U.SA K.A. Ribet Department of… See more details below
to Linear Algebra Second Edition With 66 Illustrations i Springer Serge Lang Department of Mathematics Yale University New Haven, CT 06520 U.SA Editorial Board S. Axler F. W. Gehring Department of Mathematics Department of Mathematics Michigan State University U niversity of Michigan East Lansing, MI 48824 Ann Arbor, MI 48019 U.SA U.SA K.A. Ribet Department of Mathematics University of California al Berkeley Berkeley, CA 94720-3840 U.S.A. Malhemalics Subjecls Classificalions (2000): 15-01 ISBN 978-1-4612-7002-7 ISBN 978-1-4612-1070-2 (eBook) DOI 10.1007/978-1-4612-1070-2 Library of Congress Cataloging in Publication Dala Lang, Serge, 1927- Introduction to linear algebra. (Undergraduate texls in mathematics) Includes index. 1. Aigebras, Linear. 1. Tille. II. Series. QAI84.L37 1986 512'.5 85-14758 Printed on acid-free paper. The first edillOn of tlii. book was published by Addison-Wesley Publishing Company, Inc., in 1970. © 1970, 1986 by Springer Science+Business Media New York Originally published by Springer-Vedag New York, Ine. in 1986 Softcover reprint of the hardcover 2nd edition 1986 AII rights reserved. This work may not be translated or copied in whole Of in part without the written permission of the publisher Springer Science+Business Media, LLC, except for brief excerpts in connection with revÎews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, ar by similar ar dissimilar methodology now known ar hereafter dcveloped is forbidden.
Table of ContentsI Vectors.- II Matrices and Linear Equations.- III Vector Spaces.- IV Linear Mappings.- V Composition and Inverse Mappings.- VI Scalar Products and Orthogonality.- VII Determinants.- VIII Eigenvectors and Eigenvalues.- Answers to Exercises.
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This text, parts of which are drawn from Lang's Calculus of Several Variables and his more theoretical text Linear Algebra, provides a solid introduction to the subject for students of pure mathematics. The text covers vectors, matrices and systems of linear equations, vectors transformations, linear mappings, composition and inverse mappings, scalar products and orthogonality, determinants, and eigenvectors and eigenvalues. Lang demonstrates computational techniques through clearly written examples and carefully develops the basic theory. Since the emphasis is on the development of the theory, the text is best suited to students of pure mathematics. The exposition is generally clear, but at times I had to refer to the texts Beginning Linear Algebra by Blyth and Robertson and Linear Algebra by Friedberg, Insel, and Spence for clarification. The exercises include both computational problems, which require meticulous attention to detail and can sometimes be tedious, and proofs of results that extend the material developed in the text. Some problems are reintroduced after new material has been developed, enabling you to solve the problems in new ways once you have additional tools at your disposal. Answers to most of the exercises are provided in an appendix, making the text suitable for self-study. Since this text was designed for a one semester class for students who have not necessarily completed multi-variable calculus, its scope is limited. Students preparing to do graduate work in mathematics will need to read an additional text such as Lang's Linear Algebra, Friedberg, Insel, and Spence's Linear Algebra, Hoffman and Kunze's Linear Algebra, Axler's Linear Algebra Done Right, or Blyth and Robertson's Further Linear Algebra.