# Monomial matrix

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Monomial matrix.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Monomial_matrix&oldid=39093

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