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Group Superset Field Matrix Subgroup Square Matrix Finite Field Invertible Linear Transformation Matrix Operations Diagonal Matrix Permutation Matrix

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Monomial Matrix

Let be a matrix with entries in a field . If in every row and every column 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 rows and columns such that the result is a diagonal matrix.

The $n\times n$ monomial matrices form a group under matrix multiplication. This group contains the $n\times n$ permutation matrices as a subgroup. A monomial matrix is invertible but, unlike a permutation matrix, not necessarily orthogonal. The only exception is when $K=\mathbb{F}_2$ (the finite field with elements), where the $n\times n$ monomial matrices and the $n\times n$ permutation matrices coincide.

1	Matrix
1	Field
1	Superset
1	Group
1	Subgroup
2	Square Matrix
3	Invertible Linear Transformation
3	Finite Field
4	Diagonal Matrix
4	Matrix Operations
6	Permutation Matrix