In this paper, some new upper bounds on the spectral radius of Hadamard product of nonnegative tensors are given. To show their sharpness, the comparisons among these bounds, including the existing one by Sun et al. (Linear Multilinear Algebra 66:1199–1214, 2018), are performed. We also present some lower bounds on the minimum eigenvalue of Fan product of irreducible strong \({{\mathcal {M}}}\)-tensors and their sharpness under different conditions are investigated. Some numerical examples are provided to illustrate our theoretical results.

中文翻译：

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张量的Hadamard乘积和Fan乘积的特征值的界

本文给出了非负张量Hadamard乘积谱半径的一些新的上限。为了显示它们的清晰度，比较了这些界限，包括Sun等人现有的界限。（线性多线性代数66：1199–1214，2018）。我们还给出了不可约强\（{{\ mathcal {M}}} \）-张量Fan的最小特征值的下界，并研究了它们在不同条件下的清晰度。提供一些数值示例来说明我们的理论结果。