Introduction

This introduction presents an overview of key concepts covered in the subsequent chapters of this book. The book provides a guide to elementary matrix algebra sufficient for undertaking intermediate and advanced statistical courses such as multivariate data analysis and linear models. Starting from a definition of a matrix and covering the basic rules of addition, subtraction, multiplication and inversion, the later topics include determinants, calculation of eigenvectors and eigenvalues and differentiation of linear and quadratic forms with respect to vectors. These later topics are sometimes not included in basic courses on linear algebra but are virtually essential for full discussion of statistical topics in multivariate analysis and linear models. The notes go a little beyond meeting just this need, providing an initial guide to more advanced topics such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices.