In this work firstly real semi-quaternion matrices and their properties are examined. Then, complex adjoint matrix and real matrix representation of a real semi-quaternion matrix are expressed. Further systems of linear real semi-quaternionic equations are investigated and in some of them the complex adjoint matrix and the real matrix representation are used. Moreover, matrices which entries are complex semi-quaternions and their real semi-quaternion matrix representation are presented. Additionally system of linear complex semi-quaternionic equations is described with this matrix representation. Finally, for a complex semi-quaternion matrix complex adjoint matrix is introduced. Also, linear complex semi-quaternionic equations systems are examined.