Book Review: Rao CR, Rao MB (1998) Matrix Algebra and Its Applications to Statistics and Econometrics. World Scientific, Singapore.

This is an advanced book for graduate students and researchers. It contains 16 chapters: 1 Vector Spaces; 2 Unitary and Euclidean Spaces; 3 Linear Transformations and Matrices; 4 Characteristics of Matrices; 5 Factorization of Matrices; 6 Operations of Matrices; 7 Projectors and Idempotent Operators; 8 Generalized Inverses; 9 Majorization; 10 Inequalities for Eigenvalues; 11 Matrix Approximations; 12 Optimization Problems in Statistics and Econometrics; 13 Quadratic Subspaces; 14 Inequalities with Applications in Statistics; 15 Non-Negative Matrices; 16 Miscellaneous Complements. The book provides a self-contained, updated and unified treatment of the theory and applications of matrix methods in statistics and econometrics, including a large number of examples and complements. It is presented in such a clear way that definitions, properties, propositions, theorems, proofs, examples and complements are given step by step in sections. No solutions are provided for the complements, though some are followed by a hint. Additional notes on the references and sources of the material are attached at the ends of most chapters.