## Permutation Matrices

A permutation matrix is a square matrix with a
1. 1 in each row and all other entries in that row equal to zero.
2. 1 in each column and all other entries in that column equal to zero.
A permutation matrix reorders the components of a vector.
Example:
$\left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{array} \right) \begin{pmatrix}x_1\\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix}x_2 \\ x_1 \\ x_3\end{pmatrix}$