Editorial Board Steven G. Krantz David Saltman (Chair) David Sattinger Ronald Stern 2000 Mathematics Subject Classification. Primary 20G15, 20G40, 11E57 Secondary 11E39, 11E88, 51N30. ABSTRACT. This is a graduate level textbook intended to introduce students to the basic facts about classical groups of linear transformations or matrices from first principles. The main pre- requisites are fairly standard courses in linear algebra and abstract algebra. Library of Congress Cataloging-in-Publication Data Grove, Larry C. Classical groups and geometric algebra / Larry C. Grove. p. cm. (Graduate studies in mathematics v. 39) Includes bibliographical references and index. ISBN 0-8218-2019-2 (alk. paper) 1. Group theory. 2. Geometry, Algebraic. I. Title. II. QA174.2 .G78 2001 512'.2—dc21 2001046251 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permission@ams.org. © 2002 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at URL: http://www.ams.org/ 10 9 8 7 6 5 4 3 2 1 07 06 05 04 03 02
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