Introduction to Matrix Analysis

2. Auflage 1987
ISBN: 978-0-89871-399-2
Verlag: Society for Industrial and Applied Mathematics

Buch, Englisch, Band 19, 430 Seiten, Format (B × H): 154 mm x 231 mm, Gewicht: 618 g

Reihe: Classics in Applied Mathematics

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.

Autoren/Hrsg.

Bellman, Richard

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Foreword; Preface to the Second Edition; Preface; 1. Maximization, Minimization, and Motivation; 2. Vectors and Matrices; 3. Diagonalization and Canonical Forms for Symmetric Matrices; 4. Reduction of General Symmetric Matrices to Diagonal Form; 5. Constrained Maxima; 6. Functions of Matrices; 7. Variational Description of Characteristic Roots; 8. Inequalities; 9. Dynamic Programming; 10. Matrices and Differential Equations; 11. Explicit Solutions and Canonical Forms; 12. Symmetric Function, Kronecker Products and Circulants; 13. Stability Theory; 14. Markoff Matrices and Probability Theory; 15. Stochastic Matrices; 16. Positive Matrices, Perron's Theorem, and Mathematical Economics; 17. Control Processes; 18. Invariant Imbedding; 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.