Let Sn denote the symmetric groupMathworldPlanetmathPlanetmath on n elements. Let χ:Sn be a complex characterMathworldPlanetmathPlanetmathPlanetmath. For any n×n matrix A=(aij)i,j=1n define the immanent of A as


Special cases of immanents are determinants and permanents — in the case where χ is the constant character (χ(x)=1 for all xSn), Immχ(A) is the permanent of A. In the case where χ is the sign of the permutationMathworldPlanetmath (which is the character of the permutation groupMathworldPlanetmath associated to the (non-trivial) one-dimensional representation), Immχ(A) is the determinant of A.

Title immanent
Canonical name Immanent
Date of creation 2013-03-22 14:05:43
Last modified on 2013-03-22 14:05:43
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 17
Author Mathprof (13753)
Entry type Definition
Classification msc 20C30
Related topic permanent
Related topic character