Main Page | See live article | Alphabetical index 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 An interesting theorem states the following: If a nonsingular matrix and its inverse are both nonnegative matrices (i.e. matrices with nonnegative entries), then the matrix is a generalized permutation matrix. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.