On Q-tensors

Parthasarathy T (), Ravindran G () and Sunil Kumar ()
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Parthasarathy T: Chennai Mathematical Institute
Ravindran G: Indian Statistical Institute
Sunil Kumar: Indian Statistical Institute

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 14, 13 pages

Abstract: Abstract 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.

Keywords: Tensor complementarity problem; Q-tensors; R-tensors; Nonnegative tensors; 90C33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02796-0

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