For an n×n matrix, let S denote any permutation e_1, e_2, ..., e_n of the set of numbers 1, 2, ..., n, and let χ^(λ)(S) be the character of the symmetric group corresponding to the partition (λ). Then the immanant ( left bracketing bar a_(m n) right bracketing bar )^(λ) is defined as ( left bracketing bar a_(m n) right bracketing bar )^(λ) = sum χ^(λ)(S) P_S where the summation is over the n! permutations of the symmetric group and P_S = a_(1e_1) a_(2e_2) ...a_(n e_n).

determinant | permanent