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This book presents matrix algebra in a way that is well-suited for those with an interest in statistics or a related discipline. It provides thorough and unified coverage of the fundamental concepts along with the specialized topics encountered in areas of statistics such as linear statistical models and multivariate analysis. It includes a number of very useful results that have only been available from relatively obscure sources. Detailed proofs are provided for all results. The style and level of presentation are designed to make the contents accessible to a broad audience. The book is essentially self-contained, though it is best-suited for a reader who has had some previous exposure to matrices (of the kind that might be acquired in a beginning course on linear or matrix algebra). It includes exercises, it can serve as the primary text for a course on matrices or as a supplementary text in courses on such topics as linear statistical models or multivariate analysis, and it will be a valuable reference.
David A. Harville is a research staff member emeritus in the Mathematical Sciences Department of the IBM T.J. Watson Research Center. Prior to joining the Research Center, he spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson, Air Force Base, Ohio), followed by twenty years as a full professor in the Department of Statistics at Iowa State University. He has extensive experience in the area of linear statistical models, having taught (on numberous occasions) M.S.- and Ph.D.-level courses on that topic, having been the thesis adviser of ten Ph.D. students, and having authored more than 70 research articles. His work has been recognized by his having been named a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics, by his election as a member of the International Statistical Institute, and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.
Preface. - Matrices. - Submatrices and partitioned matricies. - Linear dependence and independence. - Linear spaces: row and column spaces. - Trace of a (square) matrix. - Geometrical considerations. - Linear systems: consistency and compatability. - Inverse matrices. - Generalized inverses. - Indepotent matrices. - Linear systems: solutions. - Projections and projection matrices. - Determinants. - Linear, bilinear, and quadratic forms. - Matrix differentiation. - Kronecker products and the vec and vech operators. - Intersections and sums of subspaces. - Sums (and differences) of matrices. - Minimzation of a second-degree polynomial (in n variables) subject to linear constraints. - The Moore-Penrose inverse. - Eigenvalues and Eigenvectors. - Linear transformations. - References. - Index.