AN INEQUALITY FOR POSITIVE-DEFINITE MATRICES WITH APPLICATIONS TO COMBINATORIAL MATRICES

If A is an element of M-n(C) is a positive definite Hermitian matrix, d the average of the diagonal entries of A, and f the average of the a bsolute values of the off-diagonal entries of A, then det A less than or equal to (d - f)(n-1)[d + (n -1)f]. As a corollary we obtain a stre ngthening of Hadamard's inequality for positive definite matrices. The results can be used to prove inequalities for the determinants of (+/ -1) matrices, (0, 1) matrices, positive matrices, stochastic matrices, and constant-column-sum matrices. (C) 1997 Elsevier Science Inc.