基本説明
New in paperback. Hardcover was published in 2007.
Full Description
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics, especially the areas of linear statistical models and multivariate statistics. This reference book provides the background in matrix algebra necessary to do research and understand the results in these areas. Essentially self-contained, the book is best-suited for a reader who has had some previous exposure to matrices. Solultions to the exercises are available in the author's "Matrix Algebra: Exercises and Solutions."
Contents
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.
