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A complete, self-contained introduction to matrix analysis theory and practice Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. As such, they have become a vital part of any statistical education. Unfortunately, matrix methods are usually treated piecemeal in courses on everything from regression analysis to stochastic processes. Matrix Analysis for Statistics offers a unique view of matrix analysis theory and methods as a whole. Professor James R. Schott provides in-depth, step-by-step coverage of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors, the Moore-Penrose inverse, matrix differentiation, the distribution of quadratic forms, and more. The subject matter is presented in a theorem/proof format, and every effort has been made to ease the transition from one topic to another. Proofs are easy to follow, and the author carefully justifies every step. Accessible even for readers with a cursory background in statistics, the text uses examples that are familiar and easy to understand. Other key features that make this the ideal introduction to matrix analysis theory and practice include: Self-contained chapters for flexibility in topic choice. Extensive examples and chapter-end practice exercises. Optional sections for mathematically advanced readers.
| Price | Condition | Delivery | Seller | Action |
| $110.00 | Digital |
| WonderClub |
Mark Guindon
reviewed Matrix analysis for statistics on January 24, 2015
Matrix analysis for statistics
If queried, the mathematician that does not work in statistics will most likely not feel that there is a need for a separate course in matrices applied to statistics. There is no doubt that statisticians need to know a great deal about matrices, so the question comes down to whether the traditional math courses in linear algebra are sufficient. In either case, it is still of benefit to have one source that statisticians can consult as a reference for problems with matrices and this book can serve as that source.
Mathematicians with little experience in statistics will have no difficulty in understanding the contents of the book, as nearly all of it is mathematical rather than statistical in nature. The first three chapters are:
*) A review of elementary matrix algebra.
*) Vector spaces.
*) Eigenvalues and eigenvectors.
With the exception of ten pages devoted to random vectors in chapter 1, there were few major items gleaned from statistics. They could serve as the first three chapters of any book on matrix operations. While the remaining chapters do contain more statistical concepts, the overwhelming majority of the material does not involve problems in statistics. There are a large number of problems at the end of the chapters and solutions are not provided.
The remaining chapters are:
*) Matrix factorizations and matrix norms.
*) Generalized inverses.
*) Systems of linear equations.
*) Partitioned matrices.
*) Special matrices and matrix products.
*) Matrix derivatives and related topics.
*) Some special topics related to quadratic forms.
The level of difficulty is within the reach of an advanced undergraduate, although it was written for graduate students in statistics. In my opinion, previous experience in statistics would be helpful, but not required for a reader to understand the material. If you are looking for a book on matrix operations, this one will serve your purpose, independent of whether your focus is on statistics.
Published in Journal of Recreational Mathematics, reprinted with permission and this review appears on Amazon.
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