A general method for solving linear elliptic biquaternion equations

Abstract

In this paper, $8\times 8$ real matrix representations of elliptic biquaternions are obtained and by means of these representations, a general method is developed to solve the linear elliptic biquaternion equations. Then, this method is applied to the well-known quaternion equations X−QXR = S and QX−XR = S over the elliptic biquaternion algebra. Also, some illustrative numerical examples are given to show how this method works. Moreover, numerical algorithms for the problems considered in this study are provided. Elliptic biquaternion algebra is generalized form of complex quaternion algebra and so real quaternion algebra. Therefore, the results given in this paper generalize and complement some known results from the literature.

COMMUNICATED BY:

• T. Qian

Keywords:

• Elliptic biquaternion
• quaternion equation
• solution
• real representation

AMS SUBJECT CLASSIFICATION:

• 11R52

Acknowledgments

The authors would like to thank Professor Mehmet Ali Güngör and Associate Professor Mahmut Akyi$\tilde{g}$it for their useful discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).