Matrix analysis for statistics. 2nd ed.

*(English)*Zbl 1076.15002
Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley-Interscience (ISBN 0-471-66983-0/hbk). xvi, 456 p. (2005).

The first edition of this book appeared in 1997 and was reviewed by the present reviewer. [Matrix analysis for statistics. Wiley Series in Probability and Mathematical Statistics (New York, NY: Wiley) (1997; Zbl 0872.15002)].

In this second edition the former Chapter 7 becomes Chapter 8 (and subsequent chapters are numbered accordingly). The new Chapter 7 is titled Partitioned matrices and relates to partitioning into \(2 \times 2 \) form. It contains material on determinant and inverse that was given as a section in Chapter 7 of the first edition. The author writes: “The coverage of eigenvalues in Chapter 3 has also been expanded …the last section of Chapter 3 …has now been replaced by two sections.” There are other additions, both theorems and examples, elsewhere, and over 100 new exercises. Elliptical distributions are now mentioned. Errors in the first edition have been corrected.

The list of references (118 items) supplements the list of the first edition by about 30 items. In the case of books, some items from the former list are cited in their newer editions. Unfortunately, the reviewer’s “Non-negative matrices: An introduction to theory and applications” (1973; Zbl 0278.15011) has (still) not been cited in its second edition of 1981 (Zbl 0471.60001), which had the title “Non-negative matrices and Markov chains” and was published by Springer. A paperback photoreproduction of this 1981 book, with some additional references and Corrigenda, is in preparation by Springer.

In this second edition the former Chapter 7 becomes Chapter 8 (and subsequent chapters are numbered accordingly). The new Chapter 7 is titled Partitioned matrices and relates to partitioning into \(2 \times 2 \) form. It contains material on determinant and inverse that was given as a section in Chapter 7 of the first edition. The author writes: “The coverage of eigenvalues in Chapter 3 has also been expanded …the last section of Chapter 3 …has now been replaced by two sections.” There are other additions, both theorems and examples, elsewhere, and over 100 new exercises. Elliptical distributions are now mentioned. Errors in the first edition have been corrected.

The list of references (118 items) supplements the list of the first edition by about 30 items. In the case of books, some items from the former list are cited in their newer editions. Unfortunately, the reviewer’s “Non-negative matrices: An introduction to theory and applications” (1973; Zbl 0278.15011) has (still) not been cited in its second edition of 1981 (Zbl 0471.60001), which had the title “Non-negative matrices and Markov chains” and was published by Springer. A paperback photoreproduction of this 1981 book, with some additional references and Corrigenda, is in preparation by Springer.

Reviewer: Eugene Seneta (Sydney)

##### MSC:

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

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

15A09 | Theory of matrix inversion and generalized inverses |

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

15A06 | Linear equations (linear algebraic aspects) |

15A18 | Eigenvalues, singular values, and eigenvectors |

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

26B12 | Calculus of vector functions |

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

15A04 | Linear transformations, semilinear transformations |

15B36 | Matrices of integers |

15A23 | Factorization of matrices |

15A21 | Canonical forms, reductions, classification |

62J05 | Linear regression; mixed models |