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.
Original language | English |
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Pages (from-to) | 110-123 |
Number of pages | 14 |
Journal | Linear Algebra and Its Applications |
Volume | 510 |
DOIs | |
Publication status | Published - 1 Dec 2016 |
Keywords
- (0,1) tensor
- Completely positive tensor
- Multi-hypergraph
- {0,1} completely positive tensor
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics