INEQUALITIES FOR DIAGONALLY DOMINANT MATRICES.

Let A = (a_ij) and H = (h_ij) be positive semidefinite matrices of the same order. If a_ij ≥ |h_ij| 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]