A general method for solving linear matrix equations of elliptic biquaternions with applications

Abstract

In this study, we obtain the real representations of elliptic biquaternion matrices. Afterwards, with the aid of these representations, we develop a general method to solve the linear matrix equations over the elliptic biquaternion algebra. Also we apply this method to the well known matrix equations X - AXB = C and AX - XB = C over the elliptic biquaternion algebra. Then, we give some illustrative numerical examples to show how the aforementioned method and its results work. Furthermore, we provide numerical algorithms for all the problems considered in this paper. Elliptic biquaternions are generalized form of complex quaternions and so real quaternions. This relation is valid for their matrices, as well. Thus, the obtained results extend, generalize and complement some known results from the literature.

Keywords

• elliptic biquaternion
• matrices of elliptic biquaternions
• matrix equation
• solution
• real representation