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Let A = (aij) and H = (hij) be positive semidefinite matrices of the same order. If aij ≥ |hij| for all i, j; A is diagonally dominant and all row sums of H are equal to zero, then we show that the sum of all k x k principal minors of A is greater than or equal to the sum of all k x k principal minors of H. [ABSTRACT FROM AUTHOR]