Abstract :
If is a positive definite Hermitian matrix, d the average of the diagonal entries of A, and f the average of the absolute values of the off-diagonal entries of A, then det A (d − f)n−1[d + (n − 1)f]. As a corollary we obtain a strengthening of Hadamardʹs 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.
