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

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...

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Detalles Bibliográficos
Autores principales: Zhou, Lixin, Liu, Jianzhou, Zhu, Li
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5607157/
https://www.ncbi.nlm.nih.gov/pubmed/28989258
http://dx.doi.org/10.1186/s13660-017-1499-4
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author Zhou, Lixin
Liu, Jianzhou
Zhu, Li
author_facet Zhou, Lixin
Liu, Jianzhou
Zhu, Li
author_sort Zhou, Lixin
collection PubMed
description 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.
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spelling pubmed-56071572017-10-05 The closure property of [Formula: see text] -tensors under the Hadamard product Zhou, Lixin Liu, Jianzhou Zhu, Li J Inequal Appl Research 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. Springer International Publishing 2017-09-20 2017 /pmc/articles/PMC5607157/ /pubmed/28989258 http://dx.doi.org/10.1186/s13660-017-1499-4 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhou, Lixin
Liu, Jianzhou
Zhu, Li
The closure property of [Formula: see text] -tensors under the Hadamard product
title The closure property of [Formula: see text] -tensors under the Hadamard product
title_full The closure property of [Formula: see text] -tensors under the Hadamard product
title_fullStr The closure property of [Formula: see text] -tensors under the Hadamard product
title_full_unstemmed The closure property of [Formula: see text] -tensors under the Hadamard product
title_short The closure property of [Formula: see text] -tensors under the Hadamard product
title_sort closure property of [formula: see text] -tensors under the hadamard product
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5607157/
https://www.ncbi.nlm.nih.gov/pubmed/28989258
http://dx.doi.org/10.1186/s13660-017-1499-4
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