Generalized permutation matrix

In matrix theory, a generalized permutation matrix is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column.

An example of generalized permutation matrix is

<math>\begin{bmatrix}0 & 0 & 3 & 0\\ 0 & -2 & 0 & 0\\

1 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 \end{bmatrix}</math>