Matrix algebra from a statistician's perspective

著者

書誌事項

Matrix algebra from a statistician's perspective

David A. Harville

Springer, 2012, c2008

[Updated with and Errata]

  • : pbk

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注記

"Updated with and Errata 2012"--T.p.Verso

"This paperback edition, a reprint of the 1997 edition…"--Back Cover

Includes bibliographical references (p. [621]-623) and index

内容説明・目次

内容説明

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."

目次

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.

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