Matrix algebra useful for statistics. Reprint of the 1982 original.

*(English)*Zbl 1115.62006
Wiley Series in Probability and Statistics; Wiley-Interscience. Hoboken, NJ: John Wiley & Sons (ISBN 978-0-470-00961-1/pbk). xxii, 438 p. (2006).

From the preface: The purpose of this book is that of bringing to a broad spectrum of readers a knowledge of matrix algebra that is useful in the statistical analysis of data and in statistics generally. The basic prerequisite for using the book is high school algebra. Differential calculus is used on only a few pages, which can easily be omitted; nothing will be lost insofar as a general understanding of matrix algebra is concerned. Proofs and demonstrations of most of the theory are given, for without them the presentation would be lifeless. But in every chapter the theoretical development is profusely illustrated with elementary numerical examples and with illustrations taken from a variety of applied sciences. And the last three chapters are devoted solely to uses of matrix algebra in statistics, with Chapters 14 and 15 outlining two of the most widely used statistical techniques: regression and linear models.

The mainstream of the book is its first eleven chapters, beginning with one on introductory concepts that includes a discussion of subscript and summation notation. This is followed by four chapters dealing with basic arithmetic, special matrices, determinants and inverses. Chapters 6 and 7 are on rank and canonical forms, 8 and 9 deal with generalized inverses and solving linear equations, 10 is a collection of results on partitioned matrices and 11 describes eigenvalues and eigenvectors. Background theory for Chapter 11 is collected in an appendix, Chapter 11A, some summaries and miscellaneous topics make up Chapter 12, statistical illustrations constitute Chapter 13, and Chapters 14 and 15 describe regression and linear models. All chapters except the last two end with exercises.

The mainstream of the book is its first eleven chapters, beginning with one on introductory concepts that includes a discussion of subscript and summation notation. This is followed by four chapters dealing with basic arithmetic, special matrices, determinants and inverses. Chapters 6 and 7 are on rank and canonical forms, 8 and 9 deal with generalized inverses and solving linear equations, 10 is a collection of results on partitioned matrices and 11 describes eigenvalues and eigenvectors. Background theory for Chapter 11 is collected in an appendix, Chapter 11A, some summaries and miscellaneous topics make up Chapter 12, statistical illustrations constitute Chapter 13, and Chapters 14 and 15 describe regression and linear models. All chapters except the last two end with exercises.