A square matrix over an associative ring with identity, in each row and column of which there is exactly one non-zero element. If the non-zero entries of a monomial matrix are equal to $1$, then the matrix is called a permutation matrix. Any monomial matrix is the product of a permutation matrix and a diagonal matrix.
Monomial matrix. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Monomial_matrix&oldid=39093