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 Superieure de Lyon.
Denis Serre is Professor of Mathematics at Ecole Normale Superieure 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: Theorie et Pratique, published by Dunod (2001).
Preface to the First Edition.
List of Symbols.
1 Elementary Linear and Multilinear Algebra.
2 What Are Matrices.
3 Square Matrices.
4 Tensor and Exterior Products.
5 Matrices with Real or Complex Entries.
6 Hermitian Matrices.
8 Nonnegative Matrices.
9 Matrices with Entries in a Principal Ideal Domain; Jordan Reduction.
10 Exponential of a Matrix, Polar Decomposition, and Classical Groups.
11 Matrix Factorizations and Their Applications.
12 Iterative Methods for Linear Systems.
13 Approximation of Eigenvalues.
Index of Notation.
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