张量互补问题解集的一些性质
Some Prooreties of Solution Sets for Tensor Complementarity Problems
摘要: 张量互补问题成为现如今张量理论研究的热点课题之一，其主体结构为各种结构结构张量的性质及其与张量互补问题的相互联系，从而得到互补问题解集的性质。在这篇论文中，我们主要研究了列充分张量的部分性质。讨论列充分张量对角元素的特性。该研究将列充分的性质从矩阵扩展到张量。同时通过引入辅助矩阵，得到偶阶行对角张量互补问题与线性互补问题之间的关系，将张量互补问题解集的有限性和唯一性与其对应的辅助矩阵和主化矩阵互补问题的有限性和唯一性相联系。
Abstract: The problem of tensor complementarity has become one of the hot topics in tensor theory. Its main structure is the properties of various structural tensors and their interrelation with the tensor complementation problem, so as to obtain the properties of the solution set of the complementary problem. In this paper, we mainly study the partial properties of column sufficient tensors. Discuss the properties of diagonal elements of column sufficient tensors. This study extends the properties of column sufficient from matrices to tensors. At the same time, by introducing auxiliary matrix, we get the relationship between even order row diagonal tensor complementarity problem and linear complementarity problem. The finiteness and uniqueness of the tensor complementarity problem are related to the finiteness and uniqueness of its corresponding auxiliary matrix and principal matrix complementarity problem.
文章引用：李雪艳. 张量互补问题解集的一些性质[J]. 理论数学, 2023, 13(12): 3749-3761. https://doi.org/10.12677/PM.2023.1312388

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