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**A matrix handbook for statisticans.**
*(English)*
Zbl 1143.15001

Wiley Series in Probability and Statistics. Wiley-Interscience. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-471-74869-4/hbk). xix, 559 p. (2008).

This handbook is a MUST on a bookshelf of every statistician. It is an essential, one-of-a-kind book not only for teaching but also for everyday work of statistical researchers. On almost 600 pages the book provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. 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; 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. This handbook addresses the needs for matrix theory topics to be presented together in one book and features a collection of topics not found up to now elsewhere under one cover. These topics include: Complex matrices; A wide range of special matrices; Special products and operators of matrices; Partitioned and patterned matrices; Matrix approximations; Matrix optimization; Random vectors and matrices; Matrix 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 where appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics.

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. This handbook addresses the needs for matrix theory topics to be presented together in one book and features a collection of topics not found up to now elsewhere under one cover. These topics include: Complex matrices; A wide range of special matrices; Special products and operators of matrices; Partitioned and patterned matrices; Matrix approximations; Matrix optimization; Random vectors and matrices; Matrix 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 where appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics.

Reviewer: Jaromir Antoch (Praha)

### MSC:

15-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to linear algebra |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |

15B52 | Random matrices (algebraic aspects) |

15A45 | Miscellaneous inequalities involving matrices |

15A03 | Vector spaces, linear dependence, rank, lineability |

15A18 | Eigenvalues, singular values, and eigenvectors |

15A15 | Determinants, permanents, traces, other special matrix functions |

15A60 | Norms of matrices, numerical range, applications of functional analysis to matrix theory |

15A09 | Theory of matrix inversion and generalized inverses |

15A06 | Linear equations (linear algebraic aspects) |