Matrix Algebra from a Statistician's Perspective

ISBN-10: 038794978X
ISBN-13: 9780387949789
Edition: 1997
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Description: 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  More...

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Book details

Copyright year: 1997
Publisher: Springer
Publication date: 11/30/2000
Binding: Hardcover
Pages: 634
Size: 6.50" wide x 9.75" long x 1.50" tall
Weight: 2.442
Language: English

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 heretofore only been available from relatively obscure sources. Detailed proofs are provided for all results. David A.Harville is a research staff memeber 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,AFB, 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 memeber 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. 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.

Preface
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
References
Index

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