The closure property of [Formula: see text]-tensors under the Hadamard product.

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Lixin Zhou, Jianzhou Liu, Li Zhu

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Lixin Zhou: School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105 P.R. China.
Jianzhou Liu: School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105 P.R. China.
Li Zhu: School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105 P.R. China.

PMID: 28989258 DOI: 10.1186/s13660-017-1499-4

In this paper, we investigate the closure property of [Formula: see text]-tensors under the Hadamard product. It is shown that the Hadamard products of Hadamard powers of strong [Formula: see text]-tensors are still strong [Formula: see text]-tensors. We then bound the minimal real eigenvalues of the comparison tensors of the Hadamard products involving strong [Formula: see text]-tensors. Finally, we show how to attain the bounds by characterizing these [Formula: see text]-tensors.

Hadamard product [Formula: see text]-tensors eigenvalues

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