Applied Linear Algebra: Electrical Networks
This chapter shows how mathematical theory is not an abstract subject which has no connection with the real world. On the contrary, this entire book is written by stating that mathematics in general, and algebra in this case, is an integrating part of eve
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Linear Algebra for Computational Sciences and Engineering
Linear Algebra for Computational Sciences and Engineering
Ferrante Neri
Linear Algebra for Computational Sciences and Engineering
Foreword by Alberto Grasso
123
Ferrante Neri Centre for Computational Intelligence De Montfort University Leicester UK and University of Jyväskylä Jyväskylä Finland
ISBN 978-3-319-40339-7 DOI 10.1007/978-3-319-40341-0
ISBN 978-3-319-40341-0
(eBook)
Library of Congress Control Number: 2016941610 © Springer International Publishing Switzerland 2016 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
We can only see a short distance ahead, but we can see plenty there that needs to be done Alan Turing
Foreword
Linear Algebra in Physics The history of linear algebra can be viewed within the context of two important traditions. The first tradition (within the history of mathematics) consists of the progressive broadening of the concept of number so to include not only positive integers, but also negative numbers, fractions, algebraic and transcendental irrationals. Moreover, the symbols in the equations became matrices, polynomials, sets, permutations. Complex numbers and vector analysis belong to this tradition. Within the development of mathematics, the one was concerned not so much about solving specific equations, but mostly about addressing general and fundamental questions. The latter were approached by extending the operations and the properties of sum and multiplication from integers to other linear algebraic structures. Different algebraic structures (Lattices and Boolean algebra) generalized other kinds of operations thus allowing to optimize some non-linear mathematical problems. As a first example, Lattices were generalizations of order relations on algebraic spaces, such as set inclusion in set theory and inequality in the
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