文献类型：期刊文献

英文题名：Some Properties of Reduced Biquaternion Tensors

作者：Liu, Ting-Ting[1,2];Yu, Shao-Wen[3]

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

年份：2024

卷号：16

期号：10

外文期刊名：SYMMETRY-BASEL

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001343211900001)】；

基金：This research was supported by the National Natural Science Foundation of China (Grant no. 12271338 and 12371023).

语种：英文

外文关键词：reduced biquaternion tensors; eigenvalues and eigentensors; complex representation

摘要：Compared to quaternions, reduced biquaternions satisfy the multiplication commutative rule and are widely employed in applications such as image processing, fuzzy recognition, image compression, and digital signal processing. However, there is little information available regarding reduced biquaternion tensors; thus, in this study, we investigate some properties of reduced biquaternion tensors. Firstly, we introduce the concept of reduced biquaternion tensors, propose the real and complex representations of reduced biquaternion tensors, and prove several fundamental theorems. Subsequently, we provide the definitions for the eigenvalues and eigentensors of reduced biquaternion tensors and present the Gersgorin theorem as it applies to their eigenvalues. Additionally, we establish the relationship between the reduced biquaternion tensor and its complex representation. Notably, the complex representation is a symmetry tensor, which significantly simplifies the process and complexity of solving for eigenvalues. Corresponding numerical examples are also provided in the paper. Furthermore, some special properties of eigenvalues of reduced biquaternion tensors are presented.