Version 1
: Received: 25 October 2024 / Approved: 28 October 2024 / Online: 29 October 2024 (09:17:54 CET)
How to cite:
Yang, L.-Q.; Wang, Q.-W.; Kou, Z. A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application. Preprints2024, 2024102162. https://doi.org/10.20944/preprints202410.2162.v1
Yang, L.-Q.; Wang, Q.-W.; Kou, Z. A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application. Preprints 2024, 2024102162. https://doi.org/10.20944/preprints202410.2162.v1
Yang, L.-Q.; Wang, Q.-W.; Kou, Z. A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application. Preprints2024, 2024102162. https://doi.org/10.20944/preprints202410.2162.v1
APA Style
Yang, L. Q., Wang, Q. W., & Kou, Z. (2024). A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application. Preprints. https://doi.org/10.20944/preprints202410.2162.v1
Chicago/Turabian Style
Yang, L., Qing-Wen Wang and Zuliang Kou. 2024 "A System of Tensor Equations over the Dual Split Quaternion Algebra with an Application" Preprints. https://doi.org/10.20944/preprints202410.2162.v1
Abstract
In this paper, we propose the definition of block tensors and the real representation of tensors. Equipped with the simplification method, i.e., the real representation along with the M-P inverse, we demonstrate the conditions that are necessary and sufficient for the system of dual split quaternion tensor equations (A*NX,X*SC)=(B,D) when its solution exists. Furthermore, the general expression of the solution is also provided when the solution of the system exists and we use a numerical example to validate it in the last section. To the best of our knowledge, it is the first time that the aforementioned tensor system has been examined on dual split quaternion algebra. Additionally, we provide its equivalent conditions when its Hermitian solution X=X* and η-Hermitian solutions X=Xη* exist. Subsequently, we discuss two special dual split quaternion tensor equations. Last but not least, we propose an application for encrypting and decrypting two color videos and we validate this algorithm through a specific example.
Keywords
dual split quaternion tensor equation; Einstein product; real representation; η-Hermitian solution; Moore-Penrose inverse
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
