## Linear Equations Systems of Real and Complex Semi-Quaternions

Iranian Journal Of Science And Technology Transaction A-Science, cilt.44, 2020 (SCI Expanded İndekslerine Giren Dergi)

• Cilt numarası: 44
• Basım Tarihi: 2020
• Doi Numarası: 10.1007/s40995-020-00956-7
• Dergi Adı: Iranian Journal Of Science And Technology Transaction A-Science

#### Özet

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