A matrix is a rectangular array of numbers or elements arranged in rows and columns. More precisely, a matrix of order, or dimension, M by N (written as M x N) is a set of M x N elements arranged in M rows and N columns. Thus, letting boldface letters denote matrices, an (M x N) matrix A may be expressed as
an ai2 ai3 ••• aiN an a22 a23 ■ ■ ■ a2N
Ami aM2 aM3
where aij is the element appearing in the ith row and the jth column of A and where [aij ] is a shorthand expression for the matrix A whose typical element is aij. The order, or dimension, of a matrix—that is, the number of rows and columns—is often written underneath the matrix for easy reference.
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