Generalized permutation matrix: Difference between revisions

Revision as of 20:24, 4 October 2009

Revision as of 21:05, 19 November 2009

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==Signed permutation group==

{{main|Hyperoctahedral group}}

A '''signed permutation matrix''' is a generalized permutation matrix whose nonzero entries are ±1, and are the integer generalized permutation matrices with integer inverse.

===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]].

* Its index 2 subgroup of matrices with determinant 1 is the Coxeter group <math>D_n</math> and is the symmetry group of the [[demihypercube]].

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