MTU Cork Library Catalogue

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Matrix algebra from a statistician's perspective / David A. Harville.

By: Harville, David A.
Material type: materialTypeLabelBookPublisher: New York : Springer, c1997Description: xvii, 630 p. : ill. ; 24 cm. + hbk.ISBN: 038794978X.Subject(s): Algebras, Linear | Linear models (Statistics)DDC classification: 512.5
Contents:
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 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 -- Minimization of a second- degree polynomial (in n variables) subject to linear constraints -- The Moore-Penrose inverse -- Eigenvalues and Eigenvectors -- Linear transformations.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
General Lending MTU Bishopstown Library Lending 512.5 (Browse shelf(Opens below)) 1 Available 00074767
Total holds: 0

Enhanced descriptions from Syndetics:

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."

Includes bibliographical references (pages 615-618) and index.

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 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 -- Minimization of a second- degree polynomial (in n variables) subject to linear constraints -- The Moore-Penrose inverse -- Eigenvalues and Eigenvectors -- Linear transformations.

Author notes provided by Syndetics

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 spent ten years as a mathematical statistician in the Applied Mathematics Research Laboratory of the Aerospace Research Laboratories (at Wright-Patterson, FB, 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 10 Ph.D. students,and having authored over 60 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 Institute and by his having served as an associate editor of Biometrics and of the Journal of the American Statistical Association.

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