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

A comprehensive, must-have handbook of matrix methods with a unique
emphasis on statistical applications

This timely book, A Matrix Handbook for Statisticians, provides
a comprehensive, encyclopedic treatment of matrices as they relate
to both statistical concepts and methodologies. Written by an
experienced authority on matrices and statistical theory, this
handbook is organized by topic rather than mathematical
developments and includes numerous references to both the theory
behind the methods and the applications of the methods. A uniform
approach is applied to each chapter, which contains four parts: a
definition followed by a list of results; a short list of
references to related topics in the book; one or more references to
proofs; and references to applications. The use of extensive
cross-referencing to topics within the book and external
referencing to proofs allows for definitions to be located easily
as well as interrelationships among subject areas to be
recognized.

A Matrix Handbook for Statisticians addresses the need for
matrix theory topics to be presented together in one book and
features a collection of topics not found elsewhere under one
cover. These topics include:

* Complex matrices

* A wide range of special matrices and their properties

* Special products and operators, such as the Kronecker
product

* Partitioned and patterned matrices

* Matrix analysis and approximation

* Matrix optimization

* Majorization

* Random vectors and matrices

* Inequalities, such as probabilistic inequalities

Additional topics, such as rank, eigenvalues, determinants,
norms, generalized inverses, linear and quadratic equations,
differentiation, and Jacobians, are also included. The book assumes
a fundamental knowledge of vectors and matrices, maintains a
reasonable level of abstraction when appropriate, and provides a
comprehensive compendium of linear algebra results with use or
potential use in statistics. A Matrix Handbook for Statisticians is
an essential, one-of-a-kind book for graduate-level courses in
advanced statistical studies including linear and nonlinear models,
multivariate analysis, and statistical computing. It also serves as
an excellent self-study guide for statistical researchers.