In this study, we generalize the definition of the Fan product of two M-matrices to any $ k $ M-matrices $ {{A}_{1}}, {{A}_{2}}, \cdots, {{A}_{k}} $ of order $ n $. We introduce two new inequalities for the lower bound of the minimum eigenvalue $ \tau \left({{A}_{1}}\star {{A}_{2}}\star \cdots \star {{A}_{k}} \right) $. These new lower bounds generalize the existing results. To validate the accuracy of our findings, we present examples in which our results outperform previous ones in certain cases.
Citation: Qin Zhong. New lower bounds of the minimum eigenvalue for the Fan product of several M-matrices[J]. AIMS Mathematics, 2023, 8(12): 29073-29084. doi: 10.3934/math.20231489
In this study, we generalize the definition of the Fan product of two M-matrices to any $ k $ M-matrices $ {{A}_{1}}, {{A}_{2}}, \cdots, {{A}_{k}} $ of order $ n $. We introduce two new inequalities for the lower bound of the minimum eigenvalue $ \tau \left({{A}_{1}}\star {{A}_{2}}\star \cdots \star {{A}_{k}} \right) $. These new lower bounds generalize the existing results. To validate the accuracy of our findings, we present examples in which our results outperform previous ones in certain cases.
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Qin Zhong. New lower bounds of the minimum eigenvalue for the Fan product of several M-matrices[J]. AIMS Mathematics, 2023, 8(12): 29073-29084. doi: 10.3934/math.20231489
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