On {0,1} CP Tensors and CP Multi-hypergraphs
arXiv:1611.09206
Abstract
A doubly nonnegative matrix can be written as a Gramian matrix, and a completely positive matrix can therefore be written as a Gramian matrix of some nonnegative vectors. In this paper, we introduce Gramian tensors and study 2-dimension completely positive tensors and {0,1} CP tensors. Also investigated are the complete positive multi-hypergraph, a generalized form of a cp graph. We also provide a necessary and sufficient condition for a 2-dimensional tensor to be completely positive.
21 pages, This research was supported by the Hong Kong Research Grant Council (No. PolyU 502111, 501212, 501913 and 15302114). The work was partially done during the first and the second authors' visit at the Hong Kong Polytechnic Uiversity in August of 2016. arXiv admin note: text overlap with arXiv:1508.04204