Matrix AnalysisSpringer Science & Business Media, 15 nov 1996 - 349 páginas A good part of matrix theory is functional analytic in spirit. This statement can be turned around. There are many problems in operator theory, where most of the complexities and subtleties are present in the finite-dimensional case. My purpose in writing this book is to present a systematic treatment of methods that are useful in the study of such problems. This book is intended for use as a text for upper division and gradu ate courses. Courses based on parts of the material have been given by me at the Indian Statistical Institute and at the University of Toronto (in collaboration with Chandler Davis). The book should also be useful as a reference for research workers in linear algebra, operator theory, mathe matical physics and numerical analysis. A possible subtitle of this book could be Matrix Inequalities. A reader who works through the book should expect to become proficient in the art of deriving such inequalities. Other authors have compared this art to that of cutting diamonds. One first has to acquire hard tools and then learn how to use them delicately. The reader is expected to be very thoroughly familiar with basic lin ear algebra. The standard texts Finite-Dimensional Vector Spaces by P.R. |
Índice
Preface | 1 |
Majorisation and Doubly Stochastic Matrices | 28 |
Variational Principles for Eigenvalues | 57 |
Symmetric Norms | 84 |
Operator Monotone and Operator Convex | 112 |
Spectral Variation of Normal Matrices | 152 |
Perturbation of Spectral Subspaces of Normal | 194 |
Spectral Variation of Nonnormal Matrices | 226 |
A Selection of Matrix Inequalities | 253 |
Perturbation of Matrix Functions | 289 |
References | 325 |
| 339 | |
Otras ediciones - Ver todo
Términos y frases comunes
Analysis applications argument assume Banach space basis Bhatia bounds called Chapter Choose closed commutes complex concave condition consider contains continuous Conversely convex Corollary corresponding decomposition defined denote derivative differentiable distance eigenvalues elements equal equation equivalent example Exercise exists expressed fact factor function given gives Hence Hermitian matrices inequality integral interval invertible Lemma Linear Algebra Appl majorisation Math matrix mean measure n x n normal normal matrices Note numbers obtained operator convex operator monotone orthonormal permutation perturbation polynomial positive positive operators Problem Proof properties Proposition proved relations representation respectively roots satisfies says Show singular values spectral statement subspaces Suppose symmetric gauge function Theorem Theory transform true unique unitarily invariant norm unitary matrix variation vector write