A permutation matrix has exactly one entry equal to one in each row and column and zeros elsewhere. Left or right multiplication permutes coordinates, and .
A signed permutation matrix has exactly one nonzero entry in each row and column, and every nonzero entry is or . It is a product of a diagonal sign matrix and a permutation matrix.
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A permutation matrix is a special type of square binary matrix that is used to represent a permutation of a finite set. Specifically, it is an \( n \times n \) matrix that contains exactly one entry of 1 in each row and each column, and all other entries are 0.