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Matrix Algebra From a Statistician's Perspective

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Produktbeschreibung

Matrix Algebra From a Statistician's Perspective

Autoren: David A. Harville
Sprache: English
Verlag: Springer-Verlag New York
ISBN: 0-387-94978-X

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.


Aus dem Inhalt:
  • 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.


Buchkategorie: Graduate/Advanced undergraduate textbook

Zielgruppe: Researchers

Bibliographie: 1st ed. 1997. Corr. 3rd printing, 2000, XVII, 630 p. 9 illus., Hardcover

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