SECONDEDITIONMATRIXANALYSISROGERA.HORN CHARLESR.JOHNSONCAMBRIDGE
MatrixAnalysisSecondEditionLinear algebra and matrix theory arefundamental tools in mathematical and physicalscience, as well as fertile fields for research.This new edition ofthe acclaimed text presentsresults of both classic and recent matrix analysis using canonical forms as a unifying theme,and demonstrates their importance in a variety of applications.The authors have thoroughly revised, updated, and expanded on the first edition. Thebook opens with an extended summary of useful concepts and facts and includes numerousnewtopicsand features,such as:.New sections on the singular value and CS decompositions.New applications of the Jordan canonical form.AnewsectionontheWeyrcanonicalformExpanded treatments of inverse problems and of block matricesAcentral role for the von Neumann tracetheorem.A new appendix with a modern list of canonical forms for a pair of Hermitianmatrices and for a symmetric-skew symmetric pair·Expanded index with more than 3,500 entries for easy referenceMore than 1,100 problems and exercises, many with hints, to reinforce understand-.ing and develop auxiliary themes such as finite-dimensional quantum systems, thecompound and adjugate matrices, and the Loewner ellipsoid:Anewappendixprovidesacollectionofproblem-solvinghintsRoger A.Horn is a Research Professor in the Department of Mathematics at the Universityof Utah.He is the author of Topics in Matrix Analysis (Cambridge University Press 1994)CharlesR.Johnson istheauthorof Topics inMatrixAnalysis(CambridgeUniversityPress1994)
Matrix Analysis Second Edition Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: New sections on the singular value and CS decompositions New applications of the Jordan canonical form A new section on the Weyr canonical form Expanded treatments of inverse problems and of block matrices A central role for the von Neumann trace theorem A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric–skew symmetric pair Expanded index with more than 3,500 entries for easy reference More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid A new appendix provides a collection of problem-solving hints. Roger A. Horn is a Research Professor in the Department of Mathematics at the University of Utah. He is the author of Topics in Matrix Analysis (Cambridge University Press 1994). Charles R. Johnson is the author of Topics in Matrix Analysis (Cambridge University Press 1994).
Matrix AnalysisSecond EditionRoger A. HornUniversity of UtahCharles R. Johnson劳究CAMBRIDGE明UNIVERSITYPRESS
Matrix Analysis Second Edition Roger A. Horn University of Utah Charles R. Johnson
CAMBRIDGEUNIVERSITYPRESSCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, Sao Paulo, Delhi, Mexico CityCambridge University Press32Avenue of the Americas, New York, NY10013-2473, USAwww.cambridge.orgInformation on this title: www.cambridge.org/9780521548236@ Roger A. Horn and Charles R. Johnson 1985, 2013This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements.no reproduction of any part may take place without the writtenpermission of Cambridge University Press.First published 1985First paperback edition 1990Second edition first published 2013Printed in the United States of AmericaAcatalog record forthispublication isavailablefromtheBritish Library.LibraryofCongressCataloginginPublicationDataHorn, Roger A.Matrix analysis / Roger A. Horn, Charles R. Johnson. 2nd ed.p.cm.Includes bibliographical references and index.ISBN978-0-521-83940-2 (hardback)1.Matrices. I. Johnson, Charles R.I. Title.QA188.H662012512.9434dc232012012300ISBN978-0-521-83940-2HardbackISBN978-0-521-54823-6 PaperbackCambridge University Press has no responsibility for the persistence or accuracy of URLs for externalorthird-party Internet Web sites referred to in this publication and does not guarantee that any contenton such Web sites is, or will remain,accurate or appropriate
cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi, Mexico City ˜ Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521548236 C Roger A. Horn and Charles R. Johnson 1985, 2013 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1985 First paperback edition 1990 Second edition first published 2013 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Horn, Roger A. Matrix analysis / Roger A. Horn, Charles R. Johnson. – 2nd ed. p. cm. Includes bibliographical references and index. ISBN 978-0-521-83940-2 (hardback) 1. Matrices. I. Johnson, Charles R. II. Title. QA188.H66 2012 512.9 434–dc23 2012012300 ISBN 978-0-521-83940-2 Hardback ISBN 978-0-521-54823-6 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate.
To the matrix theory community
To the matrix theory community