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For the Hadamard product \(A\circ A^{-1}\) of an M-matrix A and its inverse \(A^{-1}\), some new inequalities for the minimum eigenvalue of \(A\circ A^{-1}\) are derived. Numerical example is given to show that the inequalities are better than some known results.

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