Introduction to matrix analysis / Richard Bellman.

Format:

Book

Author/Creator:

Bellman, Richard, 1920-1984.

Contributor:

Society for Industrial and Applied Mathematics.

Series:

Classics in applied mathematics ; 19.

Classics in applied mathematics ; 19

Language:

English

Subjects (All):

Matrices.

Mathematical analysis.

Physical Description:

1 electronic text (xxviii, 403 p.) : ill., digital file.

Edition:

2nd ed.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1997.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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. In addition, this volume includes exercises of all levels of difficulty and many references to original papers containing further results. The problem sections contain many useful and interesting results that are not easily found elsewhere. A discussion of the theoretical treatment of matrices in the computational solution of ordinary and partial differential equations, as well as important chapters on dynamic programming and stochastic matrices are also included.

Contents:

Foreword

Preface to the Second edition

Preface

Chapter 1. Maximization, minimization, and motivation

Chapter 2. Vectors and matrices

Chapter 3. Diagonalization and canonical forms for symmetric matrices

Chapter 4. Reduction of general symmetric matrices to diagonal form

Chapter 5. Constrained maxima

Chapter 6. Functions of matrices

Chapter 7. Variational description of characteristic roots

Chapter 8. Inequalities

Chapter 9. Dynamic programming

Chapter 10. Matrices and differential equations

Chapter 11. Explicit solutions and canonical forms

Chapter 12. Symmetric function, Kronecker products and circulants

Chapter 13. Stability theory

Chapter 14. Markoff matrices and probability theory

Chapter 15. Stochastic matrices

Chapter 16. Positive matrices, Perron's theorem, and mathematical economics

Chapter 17. Control processes

Chapter 18. Invariant imbedding

Chapter 19. Numerical inversion of the Laplace transform and Tychonov regularization

Appendix A. Linear equations and rank

Appendix B. The quadratic form of Selberg

Appendix C. A method of Hermite

Appendix D. Moments and quadratic forms

Index.

Notes:

Originally published: New York : McGraw-Hill, 1970.

Includes bibliographical references and indexes.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-117-9

Publisher Number:

CL19 SIAM