Finding ways to describe many situations in mathematics and economics leads to the study of rectangular arrays of numbers. Consider, for example, the system of linear equations.

2x + 3y = 0
5x - 4y = 0

The features that characterize this system are the numerical coefficients in the equations, together with their relative positions. For this reason the system can be described by the rectangular array



which is called a matrix (plural: matrices).

Definition. A rectangular arrangement of mn numbers (real or complex) into m horizontal rows n vertical columns enclosed by a pair of brackets [ ]. such as



is called an m x n (read “m by n”) matrix or matrix of order m x n. Parentheses ( ) are also commonly used to enclose numbers constituting matrices.

The numbers forming a matrix are called elements or entries of the matrix. For the entry aij, the first subscript I specifies the row and the second subscript j, the column in which the entry appears. It must be noted that even through an m x n matrix contains mn elements, the entire matrix should be considered as a single entity. In keeping with this point of view, matrices are denoted by single capital letters such as A, B, C and so on.

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