Matrix Algebra Theory, Computations, And Applications In Statistics

Preface......Page 4
Contents......Page 11
1 Basic Vector-Matrix Structure and Notation......Page 19
2Vectors and Vector Spaces......Page 25
3Basic Properties of Matrices......Page 56
3.8.10 Singular values and the singular value decomposition......Page 142
4Vector-Matrix Derivatives and Integrals......Page 159
5Matrix Transformations and Factorizations......Page 186
6Solution of Linear Systems......Page 214
6.4 numerical accuracy......Page 231
7Evaluation of Eigenvalues and Eigenvectors......Page 253
8Special Matrices and Operations Useful in Modeling and Data Analysis......Page 270
9Selected Applications in Statistics......Page 329
10Numerical Methods......Page 380
11Numerical Linear Algebra......Page 433
12Software for Numerical Linear Algebra......Page 448
A Notation and Definitions......Page 481
BSolutions and Hints for Selected Exercises......Page 494
Index......Page 519