Generalized Permutation Matrix

In mathematics, a generalized permutation matrix (or monomial 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. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is

\begin{bmatrix}
0 & 0 & 3 & 0\\
0 & -2 & 0 & 0\\
1 & 0 & 0 & 0\\
0 & 0 & 0 & 1\end{bmatrix}.

Read more about Generalized Permutation Matrix:  Structure, Properties, Generalizations, Signed Permutation Group

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