Square Matrices of Order 2 Theory, Applications, and Problems
This unique and innovative book presents an exciting and complete detail of all the important topics related to the theory of square matrices of order 2. The readers exploring every detailed aspect of matrix theory are gently led toward understanding
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Square Matrices of Order 2 Theory, Applications, and Problems Foreword by Dennis S. Bernstein
Square Matrices of Order 2
Vasile Pop • Ovidiu Furdui
Square Matrices of Order 2 Theory, Applications, and Problems
Foreword by Dennis S. Bernstein
123
Vasile Pop Department of Mathematics Technical University of Cluj-Napoca Cluj-Napoca, Romania
Ovidiu Furdui Department of Mathematics Technical University of Cluj-Napoca Cluj-Napoca, Romania
ISBN 978-3-319-54938-5 ISBN 978-3-319-54939-2 (eBook) DOI 10.1007/978-3-319-54939-2 Library of Congress Control Number: 2017936988 Mathematics Subject Classification (2010): 15A03, 15A04, 15A09, 15A15, 15A16, 15A18, 15A21, 15A23, 15A24, 15A27, 15A60, 15A99, 15B10, 15B33, 15B36, 15B51, 15B57, 11B83, 40A05, 40A30, 97I30, 97I50 © 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
Gold, when multiplied, conspire against his master; but books, when multiplied, make great use of those who have them. —St. John Chrysostom (347–407)
He who neglects learning in his youth loses the past and is dead for the future. —Euripides (480 B.C.–406 B.C.)
To Alina O. F.
Foreword
Mathematics began with the positive integers. Next came fractions, the number zero, and negative numbers. p Attempts to extract the roots of cubic polynomials led to the imaginary unit i D 1; whose name suggests something fictitious and suspect. Beyond the complex numbers, quaternions enlist a trio of noncommuting units. Vectors arise from the need to keep track of multiple scalars, such as coordinates in a plane or three-dimensional space. Matrices, which represent linear functions on vectors, are of im
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