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单词 Immanent
释义

immanent


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

Immχ(A)=σSnχ(σ)j=1nAjσ(j).

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.

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更新时间:2025/5/4 23:37:15