A matrix, singular for matrices, is a rectangular array of numbers. Matrices naturally arise in describing a special class of functions called linear transformations. But the concept of matrices originated in the work of the two mathematicians Arthur Cayley and James Sylvester while solving a system of linear equations. In 1857, Cayley wrote Memoir on the Theory of Matrices.

A matrix can be seen as a collection of rows of numbers. Each number is called an element, or entry, of the matrix. An illustrative example of a matrix, C, is below.

The order of the numbers within the row as well as the order of the rows are important. A matrix can be described by rows and columns. C has 3 rows and 3 columns, and hence it is a 3 × 3 matrix. A 2 × 3 matrix has 2 rows and 3 columns and a 4 × 2 matrix has 4 rows and 2 columns.

The size or dimension of a matrix...