A Matrix (pl. Matrices) is an array of objects ordered in rows and columns. For the purpose of this discussion, only matrices that contain numbers will be considered.

Matrices are often used in mathematics for a vast display of purposes, many of which will be discussed later.

To begin, a matrix must be named. A matrix is most often named with a capital letter, ie. A, B, C, D…. An mxn (“m by n”) matrix is so called if it has m rows and n columns. The dimensions do not have to be equal.

/ 1 2 4 8 \
A= | 10 1 7 9 |
\ 9 3 2 5 /

The previous matrix was a 3x4 matrix because it has 3 rows and 4 columns. The dimensions of a matrix can be equal (ie. 2x2, 3x3, 4x4…). When the number of rows is equal to the number of colums, the matrix is said to be

square and of

order n.

Any given number in a matrix is called an element, or entry. Each specific element is denoted using the lowercase letter of the name of the matrix, then indicating first the row, then the column. The row and column are written subscript to the lowercase letter indicating the matrix. In the given example matrix A, a_{1 1}=1, a_{1 2}=2, a_{2 1}=10...

In constructing a matrix, it is extremly important to note that the entire array of numbers needs to be enclosed either in a large parenthesis or a large bracket. A 1x1 matrix would appear as [3] or (3), but *not* |3|. Enclosing a matrix in straight lines (pipelines) depicts an entirely different function to the numbers.

Operations for Matrices

Special Matrices