nLab monomial matrix


Linear algebra

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

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology



Paths and cylinders

Homotopy groups

Basic facts


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 08:26:26. See the history of this page for a list of all contributions to it.