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On $Q$-Tensors | | Zheng-Hai Huang
; Yun-Yang Suo
; Jie Wang
; | | Date: |
10 Sep 2015 | | Abstract: | 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
$P_0$-tensors or nonnegative tensors, four classes of tensors, i.e.,
$R_0$-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. | | Source: | arXiv, 1509.3088 | | Services: | Forum | Review | PDF | Favorites | |
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