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Let A and B be nonsingular M-matrices. Some new convergent sequences of the lower bounds of the minimum eigenvalue \(\tau(B\circ A^{-1})\) for the Hadamard product of B and \(A^{-1}\) are given. Numerical examples are given to show that these sequences are better than some known results and could reach the true value of the minimum eigenvalue in some cases.

New inequalities for the Hadamard product of an M-matrix and an inverse M-matrix