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Introduction to Matrix Analysis, Second EditionIntroduction to Matrix Analysis, Second Edition

Richard Bellman



Classics in Applied Mathematics 19

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, Kronecker 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.

Audience

Emphasizing the parts of matrix theory that occur in analysis and application, this book is invaluable to pure and applied mathematicians, physicists, engineers, economists, biologists, analysts, statisticians, and anyone concerned with modern control theory, mathematical physics, economics, and the mathematical biosciences.

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.

1997 / xxviii + 403 pages / Softcover / ISBN-13: 978-0-898713-99-2 / ISBN-10: 0-89871-399-4 /
List Price $60.50 / SIAM Member Price $42.35 / Order Code CL19
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