Matrix Algebra From a Statistician's Perspective

1. Auflage 1997. 2. printing 2008
ISBN: 978-0-387-78356-7
Verlag: Springer

Buch, Englisch, 634 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1990 g

This book offers thorough and unified coverage of the fundamental concepts of matrix algebra. Its approach will make it particularly suited to those with an interest in statistics or related disciplines. But it does much more, too: it is enlightening in specialized areas of statistics such as linear statistical models and multivariate analysis. David Harville, a former associate editor of the Journal of the American Statistical Association, ensures that the style and level of presentation make the contents accessible to a broad audience. It includes a number of very useful results that have, up to now, only been available from relatively obscure sources, and for which detailed proofs are provided. It also contains numerous exercises, the solutions to which can be found in the author’s Matrix Algebra: Exercises and Solutions.

Zielgruppe

Research

Autoren/Hrsg.

Harville, David A.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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.- Erratum.

Über Autor(innen)

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.