文献类型：期刊文献

英文题名：T-Eigenvalues of Third-Order Quaternion Tensors

作者：He, Zhuo-Heng[1,2];Deng, Mei-Ling[1];Yu, Shao-Wen[3]

机构：[1]Shanghai Univ, Newtouch Ctr Math, Dept Math, Shanghai 200444, Peoples R China;[2]Shanghai Univ, Sinoeuropean Sch Technol, Shanghai 200444, Peoples R China;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：13

期号：10

外文期刊名：MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001496361700001)】；

基金：This research is supported by the National Natural Science Foundation of China [grant numbers 12271338, 12371023, 12426508].

语种：英文

外文关键词：Hermitian; quaternion tensor; T-eigenvalue; Ger & scaron;gorin theorem

摘要：In this paper, theories, algorithms and properties of eigenvalues of quaternion tensors via the t-product termed T-eigenvalues are explored. Firstly, we define the T-eigenvalue of quaternion tensors and provide an algorithm to compute the right T-eigenvalues and the corresponding T-eigentensors, along with an example to illustrate the efficiency of our algorithm by comparing it with other methods. We then study some inequalities related to the right T-eigenvalues of Hermitian quaternion tensors, providing upper and lower bounds for the right T-eigenvalues of the sum of a pair of Hermitian tensors. We further generalize the Weyl theorem from matrices to quaternion third-order tensors. Additionally, we explore estimations related to right T-eigenvalues, extending the Ger & scaron;gorin theorem for matrices to quaternion third-order tensors.