| Summary: | In this paper, an upper bound on the spectral radius <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ρ</mi> <mo>(</mo> <mi>A</mi> <mo>∘</mo> <mi>B</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> for the Hadamard product of two nonnegative matrices (<i>A</i> and <i>B</i>) and the minimum eigenvalue <inline-formula> <math display="inline"> <semantics> <mrow> <mi>τ</mi> <mo>(</mo> <mi>C</mi> <mo>★</mo> <mi>D</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> of the Fan product of two <i>M</i>-matrices (<i>C</i> and <i>D</i>) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several <i>M</i>-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results.
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