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monomial matrix

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Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

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A monomial matrix with entries in a field FF is an n×nn \times n matrix with exactly one nonzero entry in each row and exactly one nonzero entry in each column. Under matrix multiplication, monomial matrices form a group; this group is isomorphic to a wreath product

S n(F *) nS_n \ltimes (F^\ast)^n

with respect to the canonical action of the permutation group S nS_n on the n thn^{th} power (F *) n(F^\ast)^n of the group of nonzero scalars.

The special case where the non-vanishing entries are 1 is permutation matrices

Last revised on September 13, 2018 at 04:26:26. See the history of this page for a list of all contributions to it.