Generalized permutation matrix: Difference between revisions

Revision as of 02:07, 15 December 2008

Revision as of 02:15, 15 December 2008

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==Signed permutation group==

A '''signed permutation matrix''' is a generalized permutation matrix whose nonzero entries are ±1.
===Properties===
* It is the [[Coxeter group]] <math>B_n</math>, and has order <math>2^nn!</math>.
* It is the symmetry group of the [[hypercube]] and (dually) of the [[cross-polytope]].

* It is a subgroup of the [[orthogonal group]].

==Group theory==