Algebraic Properties of Generalized Inverses
This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving t
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Dragana S. Cvetković Ilić Yimin Wei
Algebraic Properties of Generalized Inverses
Developments in Mathematics Volume 52
Series editors Krishnaswami Alladi, Gainesville, USA Hershel M. Farkas, Jerusalem, Israel
More information about this series at http://www.springer.com/series/5834
Dragana S. Cvetković Ilić Yimin Wei
Algebraic Properties of Generalized Inverses
123
Dragana S. Cvetković Ilić Faculty of Science and Mathematics University of Nis Nis Serbia
ISSN 1389-2177 Developments in Mathematics ISBN 978-981-10-6348-0 DOI 10.1007/978-981-10-6349-7
Yimin Wei School of Mathematical Sciences Fudan University Shanghai China
ISSN 2197-795X (electronic) ISBN 978-981-10-6349-7
(eBook)
Library of Congress Control Number: 2017950265 Mathematics Subject Classification (2010): 15A09, 65F20, 47L05, 47A05 © Springer Nature Singapore Pte Ltd. 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
This book gives a presentation of some current topics in theory of generalized inverses. As this theory has long been a subject of study of various authors, many of the problems and questions have been resolved. However, some have only been either partially solved or remain still open to this day. It was our goal to use this book to give a review of these efforts as well as to offer the reader possible directions for further study in this area of mathematics as well as hints at possible applications in different types of problems. This book starts with definitions of various types of generalized inverses and listing the many sorts of applications of them to different branches of both mathematics, but also to some other sc
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