Abstract
Denote by the cone of positive semidefinite hermitian n-by-n matrices. In 1918,1. Schur proved that every “normalized” generalized matrix function (GMF) dominates the determinant on The conjectured dual to Schur's Theorem is that the permanent dominates every normalized GMF on . It is shown in this article that a class of normalized GMF's is actually dominated by Hadamard's function, the product of the main diagonal elements, on
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