Some inequalities for the Hadamard product and the Fan product of matrices Original Research Article

If A and B are nonsingular M-matrices, a sharp lower bound on the smallest eigenvalue τ(Astar, filledB) for the Fan product of A and B is given, and a sharp lower bound on τ(Aring operatorB-1) for the Hadamard product of A and B-1 is derived. In addition, we also give a sharp upper bound on the spectral radius ρ(Aring operatorB) for nonnegative matrices A and B.