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In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the Ecole Normale Supérieure de Lyon.
Denis Serre is Professor of Mathematics at Ecole Normale Supérieure de Lyon and a former member of the Institut Universaire de France. He is a member of numerous editorial boards and the author of Systems of Conservation Laws (Cambridge University Press 2000). The present book is a translation of the original French edition, Les Matrices: Théorie et Pratique, published by Dunod (2001). Clear and concise introduction to matrices with elegant proofs; Of interest to scientists from many disciplines; Gives many interesting applications to different parts of mathematics, such as algebra, analysis and complexity theory; Contains 160 exercises, half of them on advanced material; Includes at least one advanced result per chapter
List of contents
Elementary Theory Square Matrices Matrices with Real or Complex Entries Norms Non-negative Matrices Matrices with Entries in a Principal Domain; Jordan's Reduction Exponential of a Matrix, Polar Decomposition and Classical Groups Matrix Factorizations Iterative Methods for Linear Problems Approximation of Eigenvalues Bibliography Index List of Symbols
