Linear Algebra and Group Theory for Physicists and Engineers
This textbook demonstrates the strong interconnections between linear algebra and group theory by presenting them simultaneously, a pedagogical strategy ideal for an interdisciplinary audience. Being approached together at the same time, these two topics
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Linear Algebra and Group Theory for Physicists and Engineers
Yair Shapira
Linear Algebra and Group Theory for Physicists and Engineers
Yair Shapira Department of Computer Science Technion, Israel Institute of Technology Haifa, Israel
ISBN 978-3-030-17855-0 ISBN 978-3-030-17856-7 https://doi.org/10.1007/978-3-030-17856-7
(eBook)
Mathematics Subject Classification (2010): 15-xx, 15Axx, 39B22, 15A60, 60J10 © Springer Nature Switzerland AG 2019 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, expressed 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. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book introduces two closely related subjects: linear algebra and group theory for undergrads in engineering, physics, chemistry, and (applied) math. This is indeed an interdisciplinary point of view: math and its applications go hand in hand. The linear algebra part introduces both vectors and matrices, with a lot of examples in two and three dimensions: small 2 2 Lorentz matrix, and 3 3 rotation matrix. This prepares the reader quite well to the group theory stuff: 2 2 Moebius and Pauli matrices, 3 3 projective matrices, and so on. This way, the reader gets ready to higher dimensions as well: big Fourier and Markov matrices, operators in quantum mechanics, and stiffness and mass matrices in (high-order) finite elements. It makes sense to place the matrices in a new group. This may help mirror (or represent) many other groups as well. This is how linear algebra paves the way to group theory. Thanks to the language of matrices, groups become much more concrete, and easy to store on the computer. Thus, the book offers a unique approach: it introduces both linear and modern algebra at the same time. This shows quite clearly how related these
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