College Algebra Matrices
Basic Definitions Concepts 1

|  |  | Definition 1 |  |
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A matrix A is a rectangular array of numbers If there are m rows and n columns, we say that the dimension of the matrix is m x n, and we refer to it as an "m by n matrix", or as a rectangular matrix. An n x n matrix is called a square matrix and is said to be of order n. An m x n matrix A is often abbreviated as A=(aij)m x n. The entry, or element, in the ith row and jth column of an m x n matrix A is denoted aij. The entries a11, a22, a33,... in a square matrix are said to be on the main diagonal of the matrix.

|  |  | Definition 2 |  |
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Two matrices are equal if they have the same dimension and if their corresponding entries are equal. If A=(aij)m x n and B=(bij)m x n then A=B if and only if aij=bij for all i and j.

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