On {0,1} CP tensors and CP pseudographs

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.