On the Solutions of Linear Elliptic Biquaternion Equations

Abstract

The real and complex quaternion algebras are isomorphic to real matrix algebras including the special types 4x4 and 8x8 real matrices, respectively. These situations are based on the fact that a finite dimensional associative algebra L over any field K is isomorphic to a subalgebra of M_n(K) where dimension of L equals n over the field K. Considering this fact and using the left Hamilton operator, we get 8x8 real matrix representations of elliptic biquaternions in this study. Then a numerical method is developed to solve the linear elliptic biquaternion equations with the aid of the aforesaid representations. Also, an illustrative example and an algorithm are provided to show how this method works.

Keywords

• Field of elliptic numbers
• Quaternion equation
• Real representation
• Solution

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