Proof of a conjecture of Fiedler and Markham
Let \(A\) be an \(n\times n\) non-singular \(M\)-matrix and let \(A \circ A^{-1}\) be the Hadamard product of \(A\) and \(A^{-1}\). The author proves that \(q(A\circ A^{-1}) \geq{2\over n}\), where \(q(A\circ A^{-1})\) is the smallest eigenvalue (in modulus) of \(A\circ A^{-1}\). This is an improvement on the lower bound obtained by the author and \textit{Z. Wang} earlier [Linear Algebra Appl. 288, 259-267 (1999; Zbl 0931.15014)]. It also settles the conjecture of \textit{M. Fiedler} and \textit{T. L. Markham} [Linear Algebra Appl. 101, 1-8 (1988; Zbl 0648.15009)].
scientific article; zbMATH DE number 1556779