Introduction

What is a matrix?

A matrix is rectangular array of scalar elements, arranged in horizontal rows and vertical columns. The dimensions (order) of a matrix are traditionally notated $m x n$, where $m$ is the number of rows and $n$ is the number of columns. For example, below is an example of a 3 x 2 matrix.

$\begin{bmatrix} a_{11} & a_{21}\\ a_{12} & a_{22} \\ a_{13} & a_{23} \end{bmatrix}$

If $m = n$, the matrix is said to be a square matrix. For example:

$\begin{bmatrix} a_{11} & a_{21}\\ a_{12} & a_{22} \end{bmatrix}$

When a matrix is assigned to a variable, it is standard to notate the variable using capital, bold-face text. For example:

$\mathbf{A} = \begin{bmatrix} a_{11} & a_{21}\\ a_{12} & a_{22} \\ a_{13} & a_{23} \end{bmatrix}$

or

$\mathbf{B} = \begin{bmatrix} a_{11} & a_{21}\\ a_{12} & a_{22} \end{bmatrix}$

You may have noticed that the elements of the matrix ($a$) are identified by position using subscript. For example $a_{11}$ or $a_{ij}$, where $i$ is the index of the row and $j$ is the index of the column.

Supplemental Video

In addition to the standard video, also check out the two practice items.

• Matrix Dimensions
• Matrix Elements