On the Consimilarity of Split Quaternions and Split Quaternion Matrices

Abstract

In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In this regard, we examine the solvability conditions and general solutions of the equations a (x) over tilde= xb and A (X) over tilde = XB in split quaternions and split quaternion matrices, respectively. Moreover, coneigenvalue and coneigenvector are defined for split quaternion matrices. Some consequences are also presented.