Singular Value Decomposition of Elliptic Quaternion Matrices: Theory and Algorithms

Hidayet Hüda Kösal; Emre Ki̇şi̇; Mahmut Akyiğit; Beyza Çelik

doi:10.20944/preprints202407.2598.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 31 July 2024 / Approved: 31 July 2024 / Online: 31 July 2024 (15:16:47 CEST)

In this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudo-inverse, and the least square problem for elliptic quaternion matrices. Moreover, we established algorithms based on these results and provided illustrative numerical experiments to substantiate the accuracy of our conclusions. In the experiments, it was observed that the p-value in the algebra of elliptic quaternions and elliptic numbers directly affects the performance of the problem under consideration. Selecting the optimal p-value for problem-solving and the elliptic behavior of many physical systems make this number system advantageous in applied sciences.

Elliptic quaternion matrix; Optimal p-value; Eigen-pairs; Singular value decomposition; Pseudo-inverse; Least square solution

Computer Science and Mathematics, Applied Mathematics

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Singular Value Decomposition of Elliptic Quaternion Matrices: Theory and Algorithms

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