Abstract

This paper resolves the following conjecture of R. Merris: Let d G λ be the generalized matrix function determined by a subgroup G of the symmetric group S m and an irreducible complex character λ of G. If A, B, and A− B are m-square positive semidefinite hermitian m-square matrices and d G λ ( A)= d G λ ( B)≠0, then A= B.

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