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Copositivity criteria of a class of fourth order 3-dimensional symmetric tensors

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摘要: In this paper, we mainly dicuss  the analytic conditions of copositivity of  a class of 4th order 3-dimensional symmetric tensors.  For a 4th order 3-dimensional symmetric tensor with its entries  $1$ or $-1$, an analytic  necessary and sufficient condition is given for its strict copositivity with the help of the properties of strictly semi-positive tensors. And by means of usual maxi-min theory,  a  necessary and sufficient condition is established for copositivity of such a  tensor also.  Applying these conclusions to a general 4th order 3-dimensional symmetric tensor,  the analytic conditions  are successfully obtained  for  verifying the (strict) copositivity, and these conditions can be very easily parsed and validated.

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[V2] 2024-07-03 21:30:40 ChinaXiv:202312.00110V2 下载全文
[V1] 2023-12-04 15:37:53 ChinaXiv:202312.00110v1 查看此版本 下载全文
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