Recently, some authors have established a number of inequalities involving the minimum eigenvalue for the Hadamard product of M -matrices. In this paper, we improve these results and give some new lower bounds on the minimum eigenvalue for the Hadamard product of an M -matrix A and its inverse A-1{A^{-1}}. Finally, it is shown by the numerical examples that our bounds are also better than some previous results.

中文翻译：

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关于 M 矩阵及其逆的 Hadamard 积的最小特征值的下界

最近，一些作者建立了一些不等式，这些不等式涉及 M 矩阵的 Hadamard 乘积的最小特征值。在本文中，我们改进了这些结果，并给出了 M 矩阵 A 及其逆 A-1{A^{-1}} 的哈达玛积的最小特征值的一些新下界。最后，数值例子表明我们的边界也比之前的一些结果更好。