Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = reduced biquaternion tensors

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
15 pages, 273 KiB  
Article
Some Properties of Reduced Biquaternion Tensors
by Ting-Ting Liu and Shao-Wen Yu
Symmetry 2024, 16(10), 1260; https://doi.org/10.3390/sym16101260 - 25 Sep 2024
Cited by 1 | Viewed by 1212
Abstract
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 [...] Read more.
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 Gersˇgorin 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. Full article
(This article belongs to the Section Mathematics)
Back to TopTop