Linear Equations Systems of Real and Complex Semi-Quaternions

Abstract

In this work firstly real semi-quaternion matrices and their properties are examined. Then, $$2n\times 2n$$ complex adjoint matrix and $$4n\times 4n$$ 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 $$2n\times 2n$$ complex adjoint matrix and the $$4n\times 4n$$ real matrix representation are used. Moreover, matrices which entries are complex semi-quaternions and their $$2n\times 2n$$ real semi-quaternion matrix representation are presented. Additionally system of linear complex semi-quaternionic equations is described with this $$2n\times 2n$$ matrix representation. Finally, for a complex semi-quaternion matrix $$4n\times 4n$$ complex adjoint matrix is introduced. Also, linear complex semi-quaternionic equations systems are examined.