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.
|Number of pages||2|
|Publication status||Published - 2000|