monomial matrix
Let be a matrix with entries in a field . If in every http://planetmath.org/node/2464row and everyhttp://planetmath.org/node/2464column of there is exactly one nonzero entry, then is amonomial matrix.
Obviously, a monomial matrix is a square matrix and there exists arearrangement of and such that the result is a diagonalmatrix
.
The monomial matrices form a group under matrixmultiplication. This group contains the permutationmatrices
as a subgroup
. A monomial matrix is invertible
but, unlike apermutation matrix, not necessarily http://planetmath.org/node/1176orthogonal
. The only exception iswhen (the finite field with elements), where the monomial matrices and the permutation matricescoincide.