2x2 Matrix Representation Forms and Inner Relationships of Split Quaternions

This paper proposes a 2x2 real matrix isomorphic representation form of split quaternions and a 2mx2n real matrix isomorphic representation form of mxn split quaternion matrices. In particular, we highlighted the inner relationships among the existing different 2x2 matrix representation forms of split quaternions. Furthermore, we studied the inner relationships among different 2x2 matrix representation forms of Hamilton quaternions as an application. The forms and relationships discussed in this paper can simplify the computation and make split quaternions get extensive applications.