Matrix Analysis for Statistics, 2nd Edition
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. This updated second edition of Matrix Analysis for Statistics offers readers a unique, unified view of matrix analysis theory and methods.
Matrix Analysis for Statistics, Second Edition provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; the distribution of quadratic forms; and more. The subject matter is presented in a theorem/proof format, allowing for a smooth transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, yet rigorous enough for students in statistics, this new edition is the ideal introduction to matrix analysis theory and practice.
The book features:
- Self-contained chapters, which allow readers to select individual topics or use the reference sequentially
- Extensive examples and chapter-end practice exercises, many of which involve the use of matrix methods in statistical analyses
- New material on elliptical distributions and new expanded coverage of such topics as eigenvalue inequalities and matrices partitioned in 2 by 2 form, in particular, results relating the rank, generalized inverse, eigenvalues of such matrices to their submatrices, and much more
- Optional sections for mathematically advanced readers
1. A Review of Elementary Matrix Algebra.
2. Vector Spaces.
3. Eigenvalues and Eigenvectors.
4. Matrix Factorizations and Martrix Norms.
5. Generalized Inverses.
6. Systems of Linear Equations.
7. Partitioned Matrices.
8. Special Matrices and Matrix Operations.
9. Matrix Derivatives and Related Topics.
10. Some Special Topics Related to Quadratic Forms.