Matrices

Theory and Applications

Denis Serre - Collection Graduate Texts in Mathematics

290 pages, parution le 01/12/2010 (2^eme édition)

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Résumé

Updated edition with 40% new content with a new and more logical structure
Features important material that was not in the first edition, including but not limited to the Dunford decomposition, tensor calculus, stable and unstable subspaces, Weyl inequalities, and von Neumann's Inequality
Includes an abundance of new exercises

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.

L'auteur - Denis Serre

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).

Autres livres de Denis Serre

Les matrices

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Sommaire

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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Denis Serre
Collection	Graduate Texts in Mathematics
Parution	01/12/2010
Édition	2^eme édition
Nb. de pages	290
Format	15 x 23,5
Couverture	Broché
Poids	601g
Intérieur	Noir et Blanc
EAN13	9781441976826
ISBN13	978-1-4419-7682-6