Geršhgorin-type theorems for <i>Z</i> <sub>1</sub> -eigenvalues of tensors with applications
Abstract In this article, we present several Geršhgorin-type theorems for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>Z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:math> {Z}_{1} -eigenvalues of tensors, which improve the results provided by Wang et al. ( Some upper bounds on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>Z</m:mi> </m:mrow> <m:mrow> <m:mi>t</m:mi> </m:mrow> </m:msub> </m:math> {Z}_{t} - eigenvalues of tensors , Appl. Math. Comput. 329 (2018), 266–277). Bounds for the largest <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>Z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:math> {Z}_{1} -eigenvalue of nonnegative tensors are given. Furthermore, based on the Geršhgorin-type theorems, we introduce some sufficient criteria for the positivity of even order tensors.
Authors
- Qian Hao (ORCID: https://orcid.org/0009-0004-0618-7352)
- Jun He (ORCID: https://orcid.org/0000-0002-1680-0235)
- Guangbin Wang (ORCID: https://orcid.org/0000-0002-1531-3275)
- Xiaowei Shen (ORCID: https://orcid.org/0000-0002-0621-4371)
Institutions
- Qingdao Agricultural University (CN)
- Guizhou Normal University (CN)
- Zunyi Normal College (CN)
Publication Details
- Journal
- Demonstratio Mathematica
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1515/dema-2025-0117
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00