A Matrix Handbook for Statisticians

George A. F. Seber9780471748694, 0471748692

This book emphasizes computational statistics and algorithms and includes numerous references to both the theory behind the methods and the applications of the methods. Each chapter consists of four parts: a definition followed by a list of results, a short list of references to related topics in the book (since some overlap is unavoidable), one or more references to proofs, and references to applications. Topics include special matrices, non-negative matrices, special products and operators, Jacobians, partitioned and patterned matrices, matrix approximation, matrix optimization, multiple integrals and multivariate distributions, linear and quadratic forms, etc.

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Table of contents :
A Matrix Handbook for Statisticians……Page 1
CONTENTS……Page 8
Preface……Page 19
1. Notation……Page 24
2. Vectors, Vector Spaces, and Convexity……Page 30
3. Rank……Page 58
4. Matrix Functions: Inverse, Transpose, Trace, Determinant, and Norm……Page 76
5. Complex, Hermitian, and Related Matrices……Page 102
6. Eigenvalues, Eigenvectors, and Singular Values……Page 114
7. Generalized Inverses……Page 148
8. Some Special Matrices……Page 170
9. Non-Negative Vectors and Matrices……Page 218
10. Positive Definite and Non-negative Definite Matrices……Page 242
11. Special Products and Operators……Page 256
12. Inequalities……Page 280
13. Linear Equations……Page 302
14. Partitioned Matrices……Page 312
15. Patterned Matrices……Page 330
16. Factorization of Matrices……Page 346
17. Differentiation……Page 374
18. Jacobians……Page 406
19. Matrix Limits, Sequences, and Series……Page 440
20. Random Vectors……Page 450
21. Random Matrices……Page 484
22. Inequalities for Probabilities and Random Variables……Page 518
23. Majorization……Page 530
24. Optimization and Matrix Approximation……Page 538
References……Page 552
Index……Page 570
Eagle Hill……Page 593