In this paper, we present some new results on a class of tensors, which are defined by the solvability of the corresponding tensor complementarity problem. For such structured tensors, we give a sufficient condition to guarantee the nonzero solution of the corresponding tensor complementarity problem with a vector containing at least two nonzero components and discuss their relationships with some other structured tensors. Furthermore, with respect to the tensor complementarity problem with a nonnegative such structured tensor, we obtain the upper and lower bounds of its solution set, and by the way, we show that the eigenvalues of such a tensor are closely related to this solution set.

中文翻译：

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结构化张量的性质和互补问题

在本文中，我们提出了一类张量的一些新结果，这些结果由相应张量互补问题的可解性定义。对于这样的结构化张量，我们给出了一个充分条件来保证对应张量互补问题的非零解具有一个包含至少两个非零分量的向量，并讨论它们与其他一些结构化张量的关系。此外，对于非负的这种结构化张量的张量互补问题，我们得到了其解集的上下界，并顺便证明了这种张量的特征值与该解集密切相关。