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A Matrix Handbook for Statisticians, by George A. F. Seber
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A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications
This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized.
A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include:
-
Complex matrices
-
A wide range of special matrices and their properties
-
Special products and operators, such as the Kronecker product
-
Partitioned and patterned matrices
-
Matrix analysis and approximation
-
Matrix optimization
-
Majorization
-
Random vectors and matrices
-
Inequalities, such as probabilistic inequalities
Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.
- Sales Rank: #1735233 in Books
- Published on: 2007-11-27
- Original language: English
- Number of items: 1
- Dimensions: 9.60" h x 1.40" w x 6.50" l, 2.11 pounds
- Binding: Hardcover
- 559 pages
Review
"This book maintains its uniqueness among the competition through its extensive referencing to proofs and comprehensive coverage of topics not found in any other one book." (International Statistical Review, December 2008)
"This is an authoritative and comprehensive reference that will be useful to researchers who need to use the results of matrix analysis in their work. It would also be a useful addition to the reference collection of any mathematical library." (MAA Review, March 2008)
From the Author
This book was many years in the making.� I began collecting material on the subject area several decades ago because of my interest in matrix theory and my use of it� in other statistical books that I have written. It was a hard book to write because of the breadth of the subject.� After writing up � proofs for some of the results I realized that the book would be too big to include proofs and� would require� several volumes, so I decided to leave the proofs out and provide references only, except for some very short proofs not readily available. Given the extensive nature of statistical research, I have aimed for a very wide coverage including for example topics like matrices of complex numbers, Jacobians,� and stochastic matrices.
From the Back Cover
A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications
This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized.
A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include:
-
Complex matrices
-
A wide range of special matrices and their properties
-
Special products and operators, such as the Kronecker product
-
Partitioned and patterned matrices
-
Matrix analysis and approximation
-
Matrix optimization
-
Majorization
-
Random vectors and matrices
-
Inequalities, such as probabilistic inequalities
Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.
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