Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A\u25e6B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(A\u0003B) for the Fan product, and a new lower bound on the minimum eigenvalue q(B \u25e6A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.<\/p>\r\n","references":"

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