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 statisticians, engineers, biologists, and social scientists as well as those with a specifically mathematical background. Numerical methods for matrices are described and the book contains a set of algorithms to make such methods generally available. This book is intended for students of statistics and their lecturers; a wide range of users of statistics from all disciplines.