square matrix

A square matrix has the same number of rows as columns.

Examples:

1.

$\begin{pmatrix}1.00000&0.50000&0.33333&0.25000\\ 0.50000&0.33333&0.25000&0.20000\\ 0.33333&0.25000&0.20000&0.16667\\ 0.25000&0.20000&0.16667&0.14286\end{pmatrix}$
2.

$\begin{pmatrix}1\end{pmatrix}$
3.

$\begin{pmatrix}0.94&0.37&0.71&0.32&0.58\\ 0.90&0.16&0.74&0.83&0.27\\ 0.50&0.03&0.07&0.49&0.55\\ 0.15&0.59&0.43&0.03&0.76\\ 0.04&0.64&0.61&0.17&0.29\end{pmatrix}$
4.

$\begin{pmatrix}89&38&50\\ 64&26&98\\ 40&96&83\end{pmatrix}$

The notation $\operatorname{Mat}_{n}(\mathbb{K})$ is often used to signify the set of square matrices which are of order $n$ (size $n\times n$ ) with elements drawn from a field $\mathbb{K}$ . Thus, one would use $a\in\operatorname{Mat}_{3}(\mathbb{C})$ to declare that $a$ is a three-by-three matrix with elements that are complex numbers.

Property: Suppose $A$ and $B$ are matrices such that $A B$ is a square matrix. Then the product $B A$ is defined and also a square matrix.

Title	square matrix
Canonical name	SquareMatrix
Date of creation	2013-03-22 12:11:27
Last modified on	2013-03-22 12:11:27
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	9
Author	akrowne (2)
Entry type	Definition
Classification	msc 15-00