For σ\sigmaσ a permutation in SnS_nSn, the sign of σ\sigmaσ denoted sgn(σ)\text{sgn}(\sigma)sgn(σ) is the determinant of the linear transformation Pσ:Rn→RnP_\sigma:\mathbb R^n\to\mathbb R^nPσ:Rn→Rn given by Pσ(x1,…,xn)=(xσ(1),…,xσ(n)).P_\sigma(x_1,\dots,x_n) =(x_{\sigma(1)},\dots, x_{\sigma(n)}).Pσ(x1,…,xn)=(xσ(1),…,xσ(n)).
Wikidata ID: Q1064405