2015/09/10 by Zheng-Hai Huang, Zheng‐Hai Huang, Huang, Zheng-Hai +4
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Tensor decomposition and applications #math.OC
paper · pdf · doi:10.48550/arxiv.1509.03088
arxiv created 2015/09/10 · openalex publication_date 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
One of the central problems in the theory of linear complementarity problems (LCPs) is to study the class of Q-matrices since it characterizes the solvability of LCP. Recently, the concept of Q-matrix has been extended to the case of tensor, called Q-tensor, which characterizes the solvability of the corresponding tensor complementarity problem -- a generalization of LCP; and some basic results related to Q-tensors have been obtained in the literature. In this paper, we extend two famous results related to Q-matrices to the tensor space, i.e., we show that within the class of strong P0-tensors or nonnegative tensors, four classes of tensors, i.e., R0-tensors, R-tensors, ER-tensors and Q-tensors, are all equivalent. We also construct several examples to show that three famous results related to Q-matrices cannot be extended to the tensor space; and one of which gives a negative answer to a question raised recently by Song and Qi.