Abstract
A positive semidefinite 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 which are a generalized form of cp graphs. We also provide a necessary and sufficient condition for a 2-dimensional tensor to be completely positive.
Original language | English |
---|---|
Pages (from-to) | 287-306 |
Number of pages | 20 |
Journal | Linear Algebra and Its Applications |
Volume | 557 |
DOIs | |
Publication status | Published - 15 Nov 2018 |
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