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.

在这项工作中，首先检查了实半四元数矩阵及其性质。然后，表示实半四元数矩阵的\（2n \ x 2n \）复伴随矩阵和\（4n \ x 4n \）实矩阵表示。研究了线性实半四元数方程的其他系统，并在其中一些中使用了\（2n \ x 2n \）复伴随矩阵和\（4n \ x 4n \）实矩阵表示。此外，给出了条目为复半四元数的矩阵及其\（2n \乘以2n \）实半四元数矩阵表示。线性复半四元数方程组用这个\（2n \ times 2n \）描述矩阵表示。最后，针对复半四元数矩阵\（4n \乘以4n \），引入复伴随矩阵。此外，研究了线性复半四元数方程组。