monomial matrix
Let be a matrix with entries in a field . If in every http://planetmath.org/node/2464row and every http://planetmath.org/node/2464column of there is exactly one nonzero entry, then is a monomial matrix.
Obviously, a monomial matrix is a square matrix and there exists a rearrangement of and such that the result is a diagonal matrix.
The monomial matrices form a group under matrix multiplication. This group contains the permutation matrices as a subgroup. A monomial matrix is invertible but, unlike a permutation matrix, not necessarily http://planetmath.org/node/1176orthogonal. The only exception is when (the finite field with elements), where the monomial matrices and the permutation matrices coincide.
Title | monomial matrix |
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Canonical name | MonomialMatrix |
Date of creation | 2013-03-22 15:15:51 |
Last modified on | 2013-03-22 15:15:51 |
Owner | GrafZahl (9234) |
Last modified by | GrafZahl (9234) |
Numerical id | 5 |
Author | GrafZahl (9234) |
Entry type | Definition |
Classification | msc 20H20 |
Classification | msc 15A30 |
Related topic | PermutationMatrix |