Perfect Semiring of Nonnegative Matrices
In this paper, it is shown that the semiring of nonnegative matrices satisfies descending chain condition on right and left ideals, i.e., it is left or right perfect if and only if it is closed under Drazin inverse of all elements. Furthermore, each nonni
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Ravindra B. Bapat r Steve J. Kirkland r K. Manjunatha Prasad r Simo Puntanen Editors
Combinatorial Matrix Theory and Generalized Inverses of Matrices
Editors Ravindra B. Bapat Indian Statistical Institute New Delhi, India
K. Manjunatha Prasad Manipal University Manipal, Karnataka, India
Steve J. Kirkland National University of Ireland Maynooth Maynooth Co. Kildare Ireland
Simo Puntanen University of Tampere Tampere, Finland
ISBN 978-81-322-1052-8 ISBN 978-81-322-1053-5 (eBook) DOI 10.1007/978-81-322-1053-5 Springer New Delhi Heidelberg New York Dordrecht London Library of Congress Control Number: 2013932346 © Springer India 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
The success of a conference has to be evaluated by the quality of the scientific presentations and the ability of the organizers to publish the proceedings. If this is the yardstick used, I reckon the International Conference on Combinatorial Matrix Theory and Generalized Inverses of Matrices makes the grade easily. I congratulate the Department of Statistics, Manipal University, on the successful conduct of the conference and the publication of the proceedings. Manipal, India
Dr. H. Vinod Bhat
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Preface
The International Workshop and Conference on Combinatorial Matrix
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