Matrices

Theory and Applications

Denis Serre (Autor)

Buch | Softcover

289 Seiten

2012 | Softcover reprint of hardcover 2nd ed. 2010
Springer-Verlag New York Inc.
978-1-4614-2723-0 (ISBN)

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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. 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.

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).

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.

Reihe/Serie	Graduate Texts in Mathematics ; 216
Zusatzinfo	XIV, 289 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Approximation of eigenvalues • Determinant, Pfaffian • Dunford–Taylor formula • Eigenvalues, localization • Exponential, classical groups • Factorization • functional calculus • Interpolation • Invariant theory • iterative methods • Jordan reduction • Matrix norms • Normal form • Numerical range • Positive matrices • Rayleigh quotients • Singular values • stochastic matrices • Tensor and exterior calculus • Weyl's Inequalities
ISBN-10	1-4614-2723-1 / 1461427231
ISBN-13	978-1-4614-2723-0 / 9781461427230
Zustand	Neuware