Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse

For the Hadamard product A ∘ A−1 of an M-matrix A and its inverse A−1, we give new lower bounds for the minimum eigenvalue of A ∘ A−1. These bounds are strong enough to prove the conjecture of Fiedler and Markham [An inequality for the Hadamard product of an M-matrix and inverse M-matrix, Linear Algebra Appl. 101 (1988) 1–8].