On an inequality for the Hadamard product of an M-matrix and its inverse Original Research Article

When image is an M-matrix we prove the following inequality: image where Aring operatorB is the Hadamard product of two matrices A and B, q(B)=[p(B−1)]−1 and p(C) denotes the Perron eigenvalue of a nonnegative matrix C. This also gives a positive answer to the conjecture posed by Fiedler and Markham.