## About this book

### Introduction

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. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. 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 École Normale Supérieure de Lyon.

### Keywords

Approximation of eigenvalues Determinant, Pfaffian Eigenvalue Eigenvalues, localization Exponential, clas Functional calculus Invariant theory Matrix Multilinear Algebra Normal form Numerical range Singular values Tensor and exterior calculus linear algebra numerical analysis

#### Authors and affiliations

- 1.Unité de Mathématiques Pures et AppliquéÉcole Normale Supérieure de Lyon Unité de Mathématiques Pures et AppliquéLyon Cedex 07France

#### About the authors

Denis Serre is Professor of Mathematics at École Normale Supérieure de Lyon and a former member of the Institut Universitaire de France. He is a member of numerous editorial boards and the author of "Systems of Conservation Laws" (Cambridge University Press 2000). With S. Benzoni-Gavage, he is the co-author of "Multi-Dimensional Hyperbolic Partial Differential Equations. First Order Systems and Applications" (Oxford University Press 2007). With S. Friedlander, he has co-edited four volumes of a "Handbook of Mathematical Fluid Dynamics" (Elsevier 2002--2007). The first edition of the present book is a translation of the original French edition, "Les Matrices: Théorie et Pratique", published by Dunod (2001).

### Bibliographic information