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 chi^((lambda))(S) be the character of the symmetric group corresponding to the partition (lambda). Then the immanant |a_(mn)|^((lambda)) is defined as


where the summation is over the n! permutations of the symmetric group and


See also

Determinant, Permanent

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Littlewood, D. E. and Richardson, A. R. "Group Characters and Algebra." Philos. Trans. Roy. Soc. London A 233, 99-141, 1934.Littlewood, D. E. and Richardson, A. R. "Immanants of Some Special Matrices." Quart. J. Math. (Oxford) 5, 269-282, 1934.Wybourne, B. G. "Immanants of Matrices." §2.19 in Symmetry Principles and Atomic Spectroscopy. New York: Wiley, pp. 12-13, 1970.

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Cite this as:

Weisstein, Eric W. "Immanant." From MathWorld--A Wolfram Web Resource.

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