Introduction to matrix analysis

Richard Bellman9780898713992, 0898713994

Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices — symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum- maximum characterization of characteristic roots, Krnoecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools.

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Table of contents :
Introduction to Matrix Analysis:Second Edition……Page 1
Contents……Page 10
Foreword……Page 20
Preface to Second Edition……Page 22
Preface……Page 24
1 Maximization, Minimization, and Motivation……Page 32
2 Vectors and Matrices……Page 43
3 Diagonalization and Canonical Forms for Symmetric Matrices……Page 63
4 Reduction of General Symmetric Matrices to Diagonal Form……Page 75
5 Constrained Maxima……Page 104
6 Functions of Matrices……Page 121
7 Variational Description of Characteristic Roots……Page 143
10 Matrices and Differential Equations……Page 194
11 Explicit Solutions and Canonical Forms……Page 221
12 Symmetric Functions, Kronecker Products and Circulants……Page 262
13 Stability Theory……Page 280
14 Markoff Matrices and Probability Theory……Page 294
15 Stochastic Matrices……Page 312
16 Positive Matrices, Perron’s Theorem,and Mathematical Economics……Page 317
17 Control Processes……Page 347
18 Invariant Imbedding……Page 369
19 Numerical Inversion of the Laplace……Page 384
Appendix A Linear Equations and Rank……Page 402
Appendix B The Quadratic Form of Selberg……Page 410
Appendix C A Method of Her mite……Page 414
Appendix D Moments and Quadratic Forms……Page 416
Indexes……Page 422