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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author writes: “The coverage of eigenvalues in Chapter 3 has also been expanded …the last section of Chapter 3 …has now been replaced by two sections.”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.

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
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