On an inequality for the Hadamard product of an \(M\)-matrix and its inverse
Let \(A=[a_{jk}]\) be an \(n\times n\) \(M\)-matrix whose inverse is doubly stochastic. Then \[ q(A\circ A^{-1})\geq 2\max a_{kk}/(n \max a_{kk}-n+1), \] where \(\circ\) denotes the Hadamard product, \(q(B)=1/p(B^{-1})\) and \(p(C)\) is the Perron eigenvalue of a nonnegative matrix \(C\).
scientific article; zbMATH DE number 1419716