The set represents the set of elliptic numbers where is a formal quantity. An elliptic biquaternion is a linear combination of the quaternion basis with elliptic number coefficients, that is, an elliptic biquaternion is in the form where . The set of elliptic biquaternions is represented as . When , the number system and the set of elliptic biquaternions correspond to the complex numbers system and the set of complex quaternions , respectively. Thus, elliptic biquaternions are generalized form of complex and real quaternions. The real and complex quaternion algebras are isomorphic to real matrix algebras consisting special types and real matrices, respectively. These situations are based on the fact that every finite dimensional associative algebra over an arbitrary field is isomorphic with a subalgebra of with . On the other hand, the space of elliptic biquaternions is an 8-dimensional associative algebra over the real number field. Taking into consideration this case, real matrix representations of elliptic biquaternions are obtained in this study. Then a general method is developed to solve the linear elliptic biquaternion equations with the aid of these representations. Also, an illustrative numerical example is provided to show how this method works. The results given in this study generalize and complement some results which have been obtained previously for complex and real quaternions in the literature.
Anahtar Kelimeler: Field of Elliptic Numbers, Quaternion Equation, Elliptic Biquaternion, Solution, Real Representation.