Matrix Algebra: Exercises and Solutions

David A. Harville

272 pages, parution le 19/10/2001

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Résumé

This book contains over 300 exercises and solutions covering a wide variety of topics in matrix algebra. They can be used for independent study or in creating a challenging and stimulating environment that encourages active engagement in the learning process. Thus, the book can be of value to both teachers and students. The requisite background is some previous exposure to matrix algebra of the kind obtained in a first course. The exercises are those from an earlier book by the same author entitled Matrix Algebra From a Statistician's Perspective. They have been restated (as necessary) to stand alone, and the book includes extensive and detailed summaries of all relevant terminology and notation. The coverage includes topics of special interest and relevance in statistics and related disciplines, as well as standard topics. The overlap with exercises available from other sources is relatively small.

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

Some Notation
Some Terminology
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 and 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

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	David A. Harville
Parution	19/10/2001
Nb. de pages	272
Format	15,5 x 23,5
Couverture	Broché
Poids	440g
Intérieur	Noir et Blanc
EAN13	9780387953182
ISBN13	978-0-387-95318-2