2023/04/17 by Sonali Sharma, Sharma, Sonali, K. Palpandi +1 · 1 citation
Engineering · Mathematics · Medicine · #15B48 #90C30 #90C33 #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2304.08119
openalex publication_date 2023/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A tensor \mathcal A of order m and dimension n is called a \rm Q-tensor if the tensor complementarity problem has a solution for all \bf q ∈ \mathbb Rn. This means that for every vector \bf q, there exists a vector \bf u such that \bf u ≥ \bf 0,\bf w = \mathcal A\bf um-1+\bf q ≥ \bf 0,~and~ \bf uT\bf w = 0. In this paper, we prove that within the class of rank one symmetric tensors, the \rm Q-tensors are precisely the positive tensors. Additionally, for a symmetric \mathrm Q-tensor \mathcal A with rank(\mathcal A)=2, we show that \mathcal A is an \mathrm R0-tensor. The idea is inspired by the recent work of Parthasarathy et al. \citeParthasarathy and Sivakumar et al. \citeSivakumar on \rm Q-matrices.