matrix (mathematics)

In mathematics, a square (n × n) or rectangular (m × n) array of elements (numbers or algebraic variables) used to facilitate the study of problems in which the relation between the elements is important. They are a means of condensing information about mathematical systems and can be used for, among other things, solving simultaneous linear equations (see simultaneous equations and transformation).

The advantage of matrices is that they can be studied algebraically by assigning a single symbol to a matrix rather than considering each element separately. The symbol used is usually a bold capital letter, but often a matrix is denoted by a symbol like (a_ij), meaning ‘the matrix with element a in row i column j’. The size of a matrix is described by stating the number of its rows and then the number of its columns so, for example, a matrix with three rows and two columns is a 3 × 2 matrix. A matrix with equal numbers of rows and columns is called a ‘square matrix’.

Much early matrix theory was developed by the British mathematician Arthur Cayley, although the term was coined by his contemporary James Sylvester (1814–1897).