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Partially symmetric nonnegative rectangular tensors and copositive rectangular tensors

  • * Corresponding author: Wei Wu

    * Corresponding author: Wei Wu
This work was supported by NSF grant of China (Grant No. 11371276).
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  • In this paper, we prove a maximum property of the largest H-singular value of a partially symmetric nonnegative rectangular tensor, and establish some bounds for this singular value. Then we give the definition of copositive rectangular tensors. This concept extends from the concept of copositive square tensors. Partially symmetric nonnegative rectangular tensors and positive semi-definite rectangular tensors are examples of copositive rectangular tensors. We establish some necessary conditions and some sufficient conditions for a real partially symmetric rectangular tensor to be a copositive rectangular tensor. We also give an equivalent definition of strictly copositive rectangular tensors. Moreover, some further properties of copositive rectangular tensors are discussed.

    Mathematics Subject Classification: Primary: 15A18, 15A69, 15A72.


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