Definition:Permutation Matrix/Examples
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Examples of Permutation Matrix
$3 \times 3$ Permutation Matrix
Definition:Permutation Matrix/Examples/3 x 3
Full Rook Matrix
An $8 \times 8$ permutation matrix is known as a full rook matrix.
For example:
- $\mathbf A = \begin{bmatrix}
0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix}$
That is, it is a rook matrix in which each row and column has a $1$ in it.