Exclusion sets in eigenvalue localization sets for tensors

ABSTRACT

By excluding some proper subsets, which do not include any eigenvalues of tensors, from an existing eigenvalue localization set provided by Zhao and Sang, a new eigenvalue localization set for tensors is given. As an application, a sufficient condition such that the determinant of a tensor is not zero is provided.

KEYWORDS:

• Tensor eigenvalue
• localization set
• exclusion sets
• determinant

AMS SUBJECT CLASSIFICATIONS:

• 15A18
• 15A42
• 15A69

Acknowledgements

The authors are grateful to the referees for their useful and constructive suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Caili Sang  http://orcid.org/0000-0003-1150-4637

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant numbers 11501141 and 11601473]; Science and Technology Foundation of Guizhou Province [grant number [2015]2073]; The Applied Basic Research Programs of Science and Technology Department of Yunnan Province [grant number 2018FB001]; Natural Science Programs of Education Department of Guizhou Province [grant number [2016]066]; and Program for Excellent Young Talents in Yunnan University.