matrix

matrix in mathematics, a rectangular array of elements (e.g., numbers) considered as a single entity. A matrix is distinguished by the number of rows and columns it contains. The matrix is a 2×3 (read "2 by 3" ) matrix, because it contains 2 rows and 3 columns. A matrix having the same number of rows as columns is called a square matrix. The matrix is a 2×2 matrix, or square matrix of order 2; a square matrix of order n contains n rows and n columns. Definitions are made for certain operations with matrices; for example, a matrix may be multiplied by a number, and two matrices of the same order may be added or multiplied using an algebra of matrices that has been developed. Matrices find application in such fields as vector analysis and the solution of systems of linear equations by means of electronic computers.

Bibliography: See R. C. Dorfi, Matrix Algebra (1969).

matrix A two-dimensional array. In computing, matrices are usually considered to be special cases of n-dimensional arrays, expressed as arrays with two indices. The notation for arrays is determined by the programming language. The two dimensions of a matrix are known as its rows and columns; a matrix with m rows and n columns is said to be an m×n matrix.

In mathematics (and in this dictionary), the conventional notation is to use a capital letter to denote a matrix in its entirety, and the corresponding lower-case letter, indexed by a pair of subscripts, to denote an element in the matrix. Thus the i,jth element of a matrix A is denoted by a_ij, where i is the row number and j the column number.

A deficient two-dimensional array, in which one of the dimensions has only one index value (and is consequently elided), is a special kind of matrix known either as a row vector (with the column elided) or column vector (with the row elided). The distinction between row and column shows that the two dimensions are still significant.