Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/62146
Title: {0,1} completely positive tensors and multi-hypergraphs
Authors: Xu, C
Luo, Z
Qi, L 
Chen, Z
Keywords: (0,1) tensor
Completely positive tensor
Multi-hypergraph
{0,1} completely positive tensor
Issue Date: 2016
Publisher: North-Holland
Source: Linear algebra and its applications, 2016, v. 510, p. 110-123 How to cite?
Journal: Linear algebra and its applications 
Abstract: Completely positive graphs have been employed to associate with completely positive matrices for characterizing the intrinsic zero patterns. As tensors have been widely recognized as a higher-order extension of matrices, the multi-hypergraph, regarded as a generalization of graphs, is then introduced to associate with tensors for the study of complete positivity. To describe the dependence of the corresponding zero pattern for a special type of completely positive tensors—the {0,1} completely positive tensors, the completely positive multi-hypergraph is defined. By characterizing properties of the associated multi-hypergraph, we provide necessary and sufficient conditions for any (0,1) associated tensor to be {0,1} completely positive. Furthermore, a necessary and sufficient condition for a uniform multi-hypergraph to be a completely positive multi-hypergraph is proposed as well.
URI: http://hdl.handle.net/10397/62146
ISSN: 0024-3795
EISSN: 1873-1856
DOI: 10.1016/j.laa.2016.08.016
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