Matrix algebra from a statistician's perspective

David A. Harville

630 pages, parution le 19/04/2004

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Résumé

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.

L'auteur - David A. Harville

David A. Harville is a research staff member in the Mathematical Sciences Department of the IBM T.J. Watson Research Center. Prior to joining the Research Center, he served ten years as a mathematical statistician in the Applied Mathematics Research Laborator 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 linear statistical models, which is an area of statistics that makes heavy use of matrix algebra, and has taught (on numerous occasions) graduate-level courses on that topic. He has authored over 70 research articles. His work has been recognized by his election as a Fellow of the American Statistical Association and the Institute of Mathematical Statistics and as a member of the International Statistical Insititute.

Sommaire

Matrices
Submatrices and partitioned matrices
Linear dependence and independence
Linear spaces: Row and column spaces
Trace of a (Square) Matrix
Geometrical considerations
Linear systems
Consistency and compatibility
Inverse matrices
Generalized inverses
Idempotent matrics
Linear systems
Projections and projection matrics
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 matrics
Minimization of a second degree polynomial (in n variables) subject to linear constraints
The Moore
Penrose inverse
Eigenvalues and eigenvectors
Linear transformations

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David A. Harville
Parution	19/04/2004
Nb. de pages	630
Format	16 x 24
Couverture	Relié
Poids	1000g
Intérieur	Noir et Blanc
EAN13	9780387949789
ISBN13	978-0-387-94978-9