Upper and lower bounds for H-eigenvalues, Z-spectral radius and C-spectral radius of a third-order tensor are given by the minimax eigenvalue of symmetric matrices extracted from this given tensor. As applications, a sufficient condition for third-order nonsingular M-tensors and some valid sufficient conditions for the uniqueness and solvability of the solutions to multi-linear systems, tensor complementarity problems and non-homogeneous systems are proposed.

中文翻译：

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通过对称矩阵的极小极大值来求三阶张量的固有值

三阶张量的H特征值，Z光谱半径和C光谱半径的上限和下限由从该给定张量提取的对称矩阵的最小最大特征值给出。作为应用，提出了三阶非奇异M-张量的充分条件以及多线性系统，张量互补问题和非齐次系统解的唯一性和可解性的一些有效充分条件。