Proof of a conjecture of Fiedler and Markham Original Research Article

Let A be an n×n nonsingular M-matrix. For the Hadamard product Aring operatorA−1, M. Fiedler and T.L. Markham conjectured in [Linear Algebra Appl. 10l (1988) 1] that q(Aring operatorA−1)greater-or-equal, slanted2/n, where q(Aring operatorA−1) is the smallest eigenvalue (in modulus) of Aring operatorA−1. We considered this conjecture in [Linear Algebra Appl. 288 (1999) 259] having observed an incorrect proof in [Linear Algebra Appl. 144 (1991) 171] and obtained that q(Aring operatorA−1)greater-or-equal, slanted(2/n)(n−1)/n. The present paper gives a proof for this conjecture.