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Completely positive tensors in the complex field |
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| Authors: | Zhou Anwa Fan Jinyan Wang Qingwen |
| Institution: | 1.Department of Mathematics, Shanghai University, Shanghai, 200444, China ;2.School of Mathematical Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China ; |
| Abstract: | In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained; if it is complex completely positive, a complex completely positive decomposition can be obtained. |
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