HERMITIAN COMPLETELY POSITIVE TENSORS

摘要

In this paper, we introduce the (resp., real) Hermitian completely positive tensor, which has a (resp., real) Hermitian completely positive decomposition with all real and imaginary parts of the decomposition vectors being nonnegative (resp. real parts of the decomposition vectors being nonnegative but imaginary parts being zeros). Some properties of the (real) Hermitian completely positive tensors and (real) Hermitian copositive tensors are discussed. A semidefinite algorithm is also proposed for checking whether a Hermitian tensor is Hermitian completely positive or not. If a Hermitian tensor is not Hermitian completely positive, a certificate can be obtained; if it is, a Hermitian completely positive decomposition can be given.