Matrices
Theory and Applications
2nd Edition
Published on 26. October 2010
XIV, 289 pages
978-1-4419-7683-3 (ISBN)
Description
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.
More details
Series
Edition
Second Edition 2010
Language
English
Place of publication
New York
United States
Publishing group
Springer US
Target group
Primary & secondary/elementary & high school
Illustrations
XIV, 289 p.
File size
1,68 MB
ISBN-13
978-1-4419-7683-3 (9781441976833)
DOI
10.1007/978-1-4419-7683-3
Schweitzer Classification
Other editions
Person
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).
Content
Elementary Linear and Multilinear Algebra.- What Are Matrices.- Square Matrices.- Tensor and Exterior Products.- Matrices with Real or Complex Entries.- Hermitian Matrices.- Norms.- Nonnegative Matrices.- Matrices with Entries in a Principal Ideal Domain; Jordan Reduction.- Exponential of a Matrix, Polar Decomposition, and Classical Groups.- Matrix Factorizations and Their Applications.- Iterative Methods for Linear Systems.- Approximation of Eigenvalues.
