Introduction to matrix analysis  pbk.

Richard Bellman

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.

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[目次]

  • 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.

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この本の情報

書名 Introduction to matrix analysis
著作者等 Bellman, Richard Ernest
O'Malley Robert
Bellman Richard
シリーズ名 Classics in applied mathematics
巻冊次 pbk.
出版元 SIAM
刊行年月 c1997
版表示 2nd ed.
ページ数 xxx, 403 p.
大きさ 23 cm
ISBN 0898713994
NCID BA31843948
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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