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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2023.09.002

Complex Symmetric Tensor US-eigenvalue Inclusion Sets and Its Application

Jiangliu Gu*, Shouwei Zhou

College of Big Data and Information Engineering, Guiyang Institute of Humanities and Technology, Guiyang, Guizhou, China.

*Corresponding author: Jiangliu Gu

Published: September 27, 2023

Abstract

Professor Ni Guyan defined U-eigenvalues and US-eigenvalues in the context of geometric metric entanglement, and provided an upper bound for the number of non zero US-eigenvalues of complex tensors. In terms of its computation, the process of finding the US-eigenvalues of complex symmetric tensors is considered as an unconstrained nonlinear optimization problem in the complex domain. Bai Minru et al. proposed the Quasi-Newton method to calculate it. But in most cases, we do not need to obtain the exact value of the US-eigenvalues, only the approximate range. Liu Xia conducted research on transforming the problem of solving U and US-eigenvalues into solving Z-eigenvalues. That is to say, the inclusion set of US-eigenvalues can be given using the Z-eigenvalues inclusion set, but it is also necessary to directly provide the inclusion set of US-eigenvalues. In this paper, we will give two inclusion sets of US-eigenvalues and estimate the upper bound of Spectral radius.

Keyword

Complex symmetric tensors, US-eigenvalues, Inclusion sets, Spectral radius

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Copyright

© 2023 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
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How to cite this paper

Complex Symmetric Tensor US-eigenvalue Inclusion Sets and Its Application

How to cite this paper: Jiangliu Gu, Shouwei Zhou. (2023) Complex Symmetric Tensor US-eigenvalue Inclusion Sets and Its ApplicationJournal of Applied Mathematics and Computation7(3), 343-349.

DOI: http://dx.doi.org/10.26855/jamc.2023.09.002