Matrix Algebra Theory, Computations and Applications in Statisti
This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of
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James E. Gentle
Matrix Algebra Theory, Computations and Applications in Statistics Second Edition
Springer Texts in Statistics Series Editors Richard DeVeaux Stephen E. Fienberg Ingram Olkin
More information about this series at http://www.springer.com/series/417
James E. Gentle
Matrix Algebra Theory, Computations and Applications in Statistics Second Edition
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James E. Gentle Fairfax, VA, USA
ISSN 1431-875X ISSN 2197-4136 (electronic) Springer Texts in Statistics ISBN 978-3-319-64866-8 ISBN 978-3-319-64867-5 (eBook) DOI 10.1007/978-3-319-64867-5 Library of Congress Control Number: 2017952371 1st edition: © Springer Science+Business Media, LLC 2007 2nd edition: © Springer International Publishing AG 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 International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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Preface to the Second Edition
In this second edition, I have corrected all known typos and other errors; I have (it is hoped) clarified certain passages; I have added some additional material; and I have enhanced the Index. I have added a few more comments about vectors and matrices with complex elements, although, as before, unless stated otherwise, all vectors and matrices in this book are assumed to have real elements. I have begun to use “det(A)” rather than “|A|” to represent the determinant of A, except in a few cases. I have also expressed some derivatives as the transposes of the expressions I used formerly. I have put more conscious emphasis on “user-friendliness” in this edition. In a book, user-friendliness is primarily a function of references, both internal and external, and of the index. As an old software designer, I’ve always thought that user-friendliness i
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