Rajendra Bhatia (auth.)0387948465, 9780387948461
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. |
Table of contents :
Front Matter….Pages i-xi
A Review of Linear Algebra….Pages 1-27
Majorisation and Doubly Stochastic Matrices….Pages 28-56
Variational Principles for Eigenvalues….Pages 57-83
Symmetric Norms….Pages 84-111
Operator Monotone and Operator Convex Functions….Pages 112-151
Spectral Variation of Normal Matrices….Pages 152-193
Perturbation of Spectral Subspaces of Normal Matrices….Pages 194-225
Spectral Variation of Nonnormal Matrices….Pages 226-252
A Selection of Matrix Inequalities….Pages 253-288
Perturbation of Matrix Functions….Pages 289-323
Back Matter….Pages 325-349 |
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