实例介绍
【实例简介】
机器人广义逆的理论与应用
This page intentionally left blank adi ben-israel Thomas n.e. greville Generalized Inverses Theory and applications Second edition s Springer Adi Ben-Israel Thomas N.E. Greville(deceased) RUTCOR-Rutgcrs Centcr for Operations Research Rutgers universit Piscataway, NJ08854-8003 bisraelarutcor. rutgers. edu Editors-in-Chief Redacteurs-en-chef Jonathan borwein Peter borwein Centre for Experimental and Constructive Mathematics Department of Mathematics and Statistics Simon fraser universit Burnaby, British Columbia V5A IS6 Canada cbs-editors acms math. c With I figure Mathematics Subjcct Classification(2000): 15A09, 65FXx, 47A05 Library of Congress Cataloging-in-Publication Data Ben-Israel. adi Generalized inverses: theory and applications Adi Ben-Israel, Thomas N.E. Greville. p cm.(CMS books in mathematics: 15) Includes bibliographical references and index IsBN 0-387-00293-6(alk. paper 1. Matrix inversion. I Greville, T.N.E(Thomas Nall Eden), 1910-1998 II. Title II. Series QA188B462003 512.9434dc21 2002044506 ISBN0-387-00293-6 Printed on acid-free paper First edition published by wiley-Interscience, 1974 o 2003 Springcr-Vcrlag Ncw 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 New York, Inc, 175 Fifth Avenue, New York, NY 10010, USA), 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 sottware, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks, and similar terms, even if they arc not idcntificd as such, is not to bc taken as an cxprcssion of opinion as to whether or not they are subject to proprietary rights. Printed in the united states of america 987654321 SPIN10905616 Typesetting: Pages created by the authors using IATEX 2e www.springer-ny.com Springer-Verlag New York Berlin Heidelberg A member of Bertelsmann Springer Science+Business Media Gmbh Preface to the second edition The field of generalized inverses has grown much since the appearance of the first, edition in 1974 and is still growing. I tried to account for these developments while maintaining the informal and leisurely style of the first edition. New material was added, including a preliminary chapter ( Chap ter 0). a chapter on applications(Chapter 8), an Appendix on the work of E H. Moore, and new exercises and applications Whilc preparing this volume I compiled a bibliography on gcncralizcd inverses, posted in the webpage of the Irlernalional Linear Algebra Sociely http://www.math.technion.ac.il/iic/research.htm1 This on-line bibliography, containing over 2000 items, will be updated from timc to timc. For rcasons of spacc, many important works that appear in the on-line bibliography are not included in the bibliography of this book I apologize to the authors of these works Many colleagues helped this effort. Special thanks go to R. Bapat, S Campbell, J Miao, S K. Mitra, Y Nievergelt, R. Puystjens, A. Sidi, G.-R Wang and y. wei Tom Greville, my friend and coauthor, passed away before this project started. His scholarship and style marked the first edition and are sadly Missed i dedicate this book with love to my wife Yoki Piscataway, New Jersey adi ben-israel January 2002 This page intentionally left blank From the preface to the first edition This book is intended to provide a survey of generalized inverses from a unified point of view, illustrating the theory with applications in many ar eas. It contains more than 450 exercises at different levels of difficulty, many of which are solved in detail. This feature makes it suitable either for reference and self-study or for use as a classroom text. It can be used profitably by graduate students or advanced undergraduates, only an ele mcntary knowledge of lincar algebra bcing assur The book consisIs of an introductiOn and eight chaplers, seven of which treat generalized inverses of finite matrices, while the eighth introduces gen eralized inverses of operators between Hilbert spaces. Numerical methods are considered in Chapter 7 and in Section 9.7 While working in the area of generalized inverses, the authors have had the benefit of conversations and consultations with many colleagues. We would like to thank especially A. Charnes, R.E. Cline, P.J. Erdelsky, I Erdelyi, J.B. Hawkins, A.S. Householder, A. Lent, CC. MacDullee, M.Z Nashed, P.L. Odell, D.W. Showalter, and S. Zlobec. However, any errors that may have occurred arc the solc responsibility of the authors This book is dedicated to Abraham Charnes and Barkley rosser H a d i ben-Israel Madison. wiscon sin Thomas w e. greville September 1973 This page intentionally left blank Contents Preface to the second edition From the prcfacc to thc first editi VIl Glossary of Notation Int 1. The Inverse of a nonsingular mati 1 2. Generalized Ir 3. Illustration: Solvability of Linear SysteMs 4. Diversity of Generalized Inverses 5. Preparation Expected of the reader 4 6. Histe 4 7. Remarks on notation Suggested Further Reading 5 Chapter 0. Preliminaries 6 1. Scalars andⅤecto 6 2. Linear transformations and matrices 10 3. Elementary Operations and Permutations 22 4. The hermite normal form and related items 5. Determinants and Volume 6. Some multilinear algebra 32 7. The Jordan Normal Form 34 8. The Smith Normal Form 38 negative matrices 39 Suggested Further reading 39 Chapter 1. Existence and Construction of Generalized Inverses 40 1. The Penrose Equations 40 2. Existence and Construction of [1]-Inverses 3. Properties of [1]-Inverses 42 4. Existence and Construction of (1, 2)-Inverses 45 5. Existence and Construction of (1, 2, 3]-,(1, 2, 4] (1, 2, 3, 4]-Inverses 46 6. Explicit Formula for A 48 7. Construction of 2)-Inverses of Prescribed Rank 49 otes on Terminology Suggested Further reading 【实例截图】
【核心代码】
机器人广义逆的理论与应用
This page intentionally left blank adi ben-israel Thomas n.e. greville Generalized Inverses Theory and applications Second edition s Springer Adi Ben-Israel Thomas N.E. Greville(deceased) RUTCOR-Rutgcrs Centcr for Operations Research Rutgers universit Piscataway, NJ08854-8003 bisraelarutcor. rutgers. edu Editors-in-Chief Redacteurs-en-chef Jonathan borwein Peter borwein Centre for Experimental and Constructive Mathematics Department of Mathematics and Statistics Simon fraser universit Burnaby, British Columbia V5A IS6 Canada cbs-editors acms math. c With I figure Mathematics Subjcct Classification(2000): 15A09, 65FXx, 47A05 Library of Congress Cataloging-in-Publication Data Ben-Israel. adi Generalized inverses: theory and applications Adi Ben-Israel, Thomas N.E. Greville. p cm.(CMS books in mathematics: 15) Includes bibliographical references and index IsBN 0-387-00293-6(alk. paper 1. Matrix inversion. I Greville, T.N.E(Thomas Nall Eden), 1910-1998 II. Title II. Series QA188B462003 512.9434dc21 2002044506 ISBN0-387-00293-6 Printed on acid-free paper First edition published by wiley-Interscience, 1974 o 2003 Springcr-Vcrlag Ncw 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 New York, Inc, 175 Fifth Avenue, New York, NY 10010, USA), 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 sottware, or by similar or dissimilar methodology now known or hereafter developed is forbidden The use in this publication of trade names, trademarks, service marks, and similar terms, even if they arc not idcntificd as such, is not to bc taken as an cxprcssion of opinion as to whether or not they are subject to proprietary rights. Printed in the united states of america 987654321 SPIN10905616 Typesetting: Pages created by the authors using IATEX 2e www.springer-ny.com Springer-Verlag New York Berlin Heidelberg A member of Bertelsmann Springer Science+Business Media Gmbh Preface to the second edition The field of generalized inverses has grown much since the appearance of the first, edition in 1974 and is still growing. I tried to account for these developments while maintaining the informal and leisurely style of the first edition. New material was added, including a preliminary chapter ( Chap ter 0). a chapter on applications(Chapter 8), an Appendix on the work of E H. Moore, and new exercises and applications Whilc preparing this volume I compiled a bibliography on gcncralizcd inverses, posted in the webpage of the Irlernalional Linear Algebra Sociely http://www.math.technion.ac.il/iic/research.htm1 This on-line bibliography, containing over 2000 items, will be updated from timc to timc. For rcasons of spacc, many important works that appear in the on-line bibliography are not included in the bibliography of this book I apologize to the authors of these works Many colleagues helped this effort. Special thanks go to R. Bapat, S Campbell, J Miao, S K. Mitra, Y Nievergelt, R. Puystjens, A. Sidi, G.-R Wang and y. wei Tom Greville, my friend and coauthor, passed away before this project started. His scholarship and style marked the first edition and are sadly Missed i dedicate this book with love to my wife Yoki Piscataway, New Jersey adi ben-israel January 2002 This page intentionally left blank From the preface to the first edition This book is intended to provide a survey of generalized inverses from a unified point of view, illustrating the theory with applications in many ar eas. It contains more than 450 exercises at different levels of difficulty, many of which are solved in detail. This feature makes it suitable either for reference and self-study or for use as a classroom text. It can be used profitably by graduate students or advanced undergraduates, only an ele mcntary knowledge of lincar algebra bcing assur The book consisIs of an introductiOn and eight chaplers, seven of which treat generalized inverses of finite matrices, while the eighth introduces gen eralized inverses of operators between Hilbert spaces. Numerical methods are considered in Chapter 7 and in Section 9.7 While working in the area of generalized inverses, the authors have had the benefit of conversations and consultations with many colleagues. We would like to thank especially A. Charnes, R.E. Cline, P.J. Erdelsky, I Erdelyi, J.B. Hawkins, A.S. Householder, A. Lent, CC. MacDullee, M.Z Nashed, P.L. Odell, D.W. Showalter, and S. Zlobec. However, any errors that may have occurred arc the solc responsibility of the authors This book is dedicated to Abraham Charnes and Barkley rosser H a d i ben-Israel Madison. wiscon sin Thomas w e. greville September 1973 This page intentionally left blank Contents Preface to the second edition From the prcfacc to thc first editi VIl Glossary of Notation Int 1. The Inverse of a nonsingular mati 1 2. Generalized Ir 3. Illustration: Solvability of Linear SysteMs 4. Diversity of Generalized Inverses 5. Preparation Expected of the reader 4 6. Histe 4 7. Remarks on notation Suggested Further Reading 5 Chapter 0. Preliminaries 6 1. Scalars andⅤecto 6 2. Linear transformations and matrices 10 3. Elementary Operations and Permutations 22 4. The hermite normal form and related items 5. Determinants and Volume 6. Some multilinear algebra 32 7. The Jordan Normal Form 34 8. The Smith Normal Form 38 negative matrices 39 Suggested Further reading 39 Chapter 1. Existence and Construction of Generalized Inverses 40 1. The Penrose Equations 40 2. Existence and Construction of [1]-Inverses 3. Properties of [1]-Inverses 42 4. Existence and Construction of (1, 2)-Inverses 45 5. Existence and Construction of (1, 2, 3]-,(1, 2, 4] (1, 2, 3, 4]-Inverses 46 6. Explicit Formula for A 48 7. Construction of 2)-Inverses of Prescribed Rank 49 otes on Terminology Suggested Further reading 【实例截图】
【核心代码】
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