A Matrix Handbook for Statisticians (Wiley Series in Probability and Statistics)

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