Monomial matrix

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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.

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Monomial matrix. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.A. Suprunenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article