Work

The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications

Year: 2025

Type: article

Abstract: In this paper, considering a general solution to a system of tensor equations within the framework of the split quaternion algebra, we establish the necessary and sufficient conditions for the existence of the general solution. Furthermore, we derive the general solution for the system of tensor equations when it is solvable. In addition, we provide algorithms and numerical examples to illustrate the results presented in this study. To demonstrate the applicability of our findings, we give the algorithms and examples for the encryption and decryption of color videos. Finally, we make a conclusion.

Source: Mathematics

DOI: 10.3390/math13040644

Authors: Zong-Ru Jia, Qing-Wen Wang

Institution: Shanghai University

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: National Natural Science Foundation of China