Abstract
If A and B are n × n nonsingular M-matrices, a lower bound on the smallest eigenvalue τ ( A ☆ B ) for the Fan product of A and B is given. In addition, using the estimate on the perron root of nonnegative matrices, we also obtain an upper bound on the spectral radius ρ ( A ∘ B ) for nonnegative matrices A and B. These bounds improve some existing results.
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