Multiple regression, linear modelling, and multivariate analysis are among the most useful statistical methods for the elucidation of complicated data, and all of them are most easily explained in matrix terms. Anyone concerned with the analysis of data needs to be familiar with these methods and a knowledge of matrices is essential in order to understand the literature in which they are described. This knowledge must include some advanced topics, but can do without much of the material covered by general textbooks of matrix algebra. This book is intended to cover the necessary ground as briefly as possible. Only the simplest of basic mathematics is used, and the book should be accessible to engineers, biologists, and social scientists as well as those with a specifically mathematical background. The text of the first edition has been re-written and revised to take account of recent developments in statistical practice. The more difficult topics have been expanded and the mathematical explanations have been simplified. A new chapter has been included, at readers' request, to cover such topics as vectorising, matrix calculus and complex numbers. From the reviews of the first edition '...this should be a valuable handbook for a great variety of statistical users.' Short Book Reviews of the International Statistics Institute '...a good reference book for the serious student.' Journal of the American Statistical Association '...a very worthwhile addition to anyone's shelf. Teaching Statistics 'I recommend it.' Technometrics