# Matrix Analysis

• Rajendra Bhatia
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 169)

1. Front Matter
Pages i-xi
2. Rajendra Bhatia
Pages 1-27
3. Rajendra Bhatia
Pages 28-56
4. Rajendra Bhatia
Pages 57-83
5. Rajendra Bhatia
Pages 84-111
6. Rajendra Bhatia
Pages 112-151
7. Rajendra Bhatia
Pages 152-193
8. Rajendra Bhatia
Pages 194-225
9. Rajendra Bhatia
Pages 226-252
10. Rajendra Bhatia
Pages 253-288
11. Rajendra Bhatia
Pages 289-323
12. Back Matter
Pages 325-349

### Introduction

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.

### Keywords

algebra approximation calculus Eigenvalue exponential function inequality linear algebra matrices matrix numerical analysis operator operator theory perturbation polynomial Smooth function

#### Authors and affiliations

• Rajendra Bhatia
• 1
1. 1.Indian Statistical InstituteNew DelhiIndia

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0653-8
• Copyright Information Springer-Verlag New York, Inc. 1997
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6857-4
• Online ISBN 978-1-4612-0653-8
• Series Print ISSN 0072-5285