Permutation matrix/Definition

Permutation matrix

For a permutation ${}\pi$ on ${}\{1,\ldots ,n\}$, the ${}n\times n$-matrix

${}M_{\pi }={\left(a_{ij}\right)}\,,$

where

${}a_{\pi (j),j}=1\,$

and all other entries are ${}0$, is called a permutation matrix.