Difference between revisions of "Monomial matrix"
From Encyclopedia of Mathematics
(TeX) |
(Category:Special matrices) |
||
| Line 1: | Line 1: | ||
{{TEX|done}} | {{TEX|done}} | ||
A square [[Matrix|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|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]] | ||
Revision as of 20:32, 25 October 2014
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=31824
Monomial matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Monomial_matrix&oldid=31824
This article was adapted from an original article by D.A. Suprunenko (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article