Difference between revisions of "Monomial matrix"
From Encyclopedia of Mathematics
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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]]. | + | 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]]. |
[[Category:Special matrices]] | [[Category:Special matrices]] | ||
Latest revision as of 16:12, 11 September 2016
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://encyclopediaofmath.org/index.php?title=Monomial_matrix&oldid=36224
Monomial matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monomial_matrix&oldid=36224
This article was adapted from an original article by D.A. Suprunenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article