Completely Positive Tensors and Multi-Hypergraphs
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 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 associated tensor to be completely positive. Furthermore, a necessary and sufficient condition for a uniform multi-hypergraph to be completely positive multi-hypergraph is proposed as well.
Keywords
Cite
@article{arxiv.1508.04204,
title = {Completely Positive Tensors and Multi-Hypergraphs},
author = {Changqing Xu and Ziyan Luo and Liqun Qi},
journal= {arXiv preprint arXiv:1508.04204},
year = {2015}
}