Estimate of bounds on eigenvalues of the Hadamard product and the Fan product of matrices and nonnegative matrices

A new lower bound of the minimum eigenvalues of Hadamard product for inverse A-1 of nonsingular M -matrix A and nonsingular M -matrix B ,a new lower bound of the smallest eigenvalues of Fan product for nonsingular M -matrices A and B ,and a new supper bound of the spectral radius of Hadamard product for nonnegative matrices A and B ,are given respectively.These three estimating formulas of the bounds are easier to calculate since they only depend on the entries of matrices A and B .The given examples show that the estimating formulas of the bounds are better than several known estimating formulas.