New lower bounds of the minimum eigenvalue for the Fan product of several M-matrices

Abstract

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.

Keywords

• m-matrix
• fan product
• minimum eigenvalue
• irreducible