Completely positive tensors in the complex field

Anwa Zhou; Jinyan Fan; Qingwen Wang

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Completely positive tensors in the complex field

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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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《中国科学》 |2020年第6期|P.1219-1234|共16页
作者
Anwa Zhou; Jinyan Fan; Qingwen Wang;
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作者单位

Department of Mathematics Shanghai University Shanghai 200444 China;

School of Mathematical Sciences and MOE-LSC Shanghai Jiao Tong University Shanghai 200240 China;

Department of Mathematics Shanghai University Shanghai 200444 China;

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原文格式 PDF
正文语种 chi
中图分类张量分析;
关键词
complex completely positive tensor; complex completely positive decomposition; truncated moment problem; semidefinite program;

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专利

1. SOME REMARKS ON COMPLETELY POSITIVE MATRICES AND COMPLETELY POSITIVE GRAPHS [J] . Xiang Shuhuang (Dept.of Appl.Math.Central South UNiversityChangsha 410083PRC) . 高等学校计算数学学报：英文版 . 2000,第S1期
2. Completely Positive Definite Maps on σ-C*-algebras [J] . 许天周 ,段培超 ,郑庆琳 . 数学进展 . 2003,第002期
3. COMPLETELY POSITIVE MATRICES WITH (A)=Rank(A) [J] . Xu Changqing(Dept.of Math.Anhui UniversityHefei 230039PRC) . 高等学校计算数学学报：英文版 . 2000,第S1期
4. Effects of X-rays with or without ELF magnetic fields exposure on induction of kinetochore positive and negative micronuclei in CHO cells [C] . Ding Gui-Rong ,Guo Guo-Zheng . 第十三届全国凝聚态理论与统计物理学术会议 . 2005
5. Research on advanced PIV algorithms and their aplication in measuring complex flow fields [A] . Dr.Sheng xian Shi . 2012

Completely positive tensors in the complex field

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