Publisher Summary Matrix algebra, or more precisely, linear algebra, has a particular importance in statistics. It provides a concise means of algebraic, abstract, manipulation of arrays of data, data matrices, and it permits graphical representation of those data: almost every matrix and operation has a graphical interpretation. Thus, it provides a means of communication for the mathematician; and for the layman results can be interpreted graphically by analogy with the simple three-dimensional (Euclidean) space in which we live. This simplicity of manipulation and representation makes matrix algebra particularly suited to multivariate problems. Because multivariate statistics is concerned with manipulation of data it is important to understand the way a particular representation is obtained to gain a full interpretation. This chapter presents a discussion on the definition of structures and basic matrix operations and assembles these into forms that underlie the pattern recognition and relational methods. The chapter presents an examination on the graphical representation of vectors. Transposition of a vector or matrix is a very useful computational device. Mean-centring is a way of conveniently re-locating the origin of the space. Matrices can be regarded as collections of vectors.