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<p>A tensor is a multidimensional analog of a matrix. <i>Q</i>-matrices have been extensively studied in the context of the linear complementarity problem due to their solvability for any given vector <i>q</i>. In this article, we extend certain results of <i>Q</i>-matrices to <i>Q</i>-tensors. Characterizing a tensor as a <i>Q</i>-tensor remains a challenging problem in the literature. In this article, we establish sufficient conditions under which a principal subtensor of a <i>Q</i>-tensor is also a <i>Q</i>-tensor. Furthermore, we extend a result due to Huang, Suo and Wang. It is well-known that <i>R</i>-tensors are <i>Q</i>-tensors, although the converse does not always hold. We also provide conditions under which a <i>Q</i>-tensor can be classified as an <i>R</i>-tensor. Additionally, we prove several results pertaining to positive (nonnegative) tensors.</p>

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On Q-tensors

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Parthasarathy T,
  • Ravindran G,
  • Sunil Kumar

摘要

A tensor is a multidimensional analog of a matrix. Q-matrices have been extensively studied in the context of the linear complementarity problem due to their solvability for any given vector q. In this article, we extend certain results of Q-matrices to Q-tensors. Characterizing a tensor as a Q-tensor remains a challenging problem in the literature. In this article, we establish sufficient conditions under which a principal subtensor of a Q-tensor is also a Q-tensor. Furthermore, we extend a result due to Huang, Suo and Wang. It is well-known that R-tensors are Q-tensors, although the converse does not always hold. We also provide conditions under which a Q-tensor can be classified as an R-tensor. Additionally, we prove several results pertaining to positive (nonnegative) tensors.