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.
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Alagöz, Y., Özyurt, G. Linear Equations Systems of Real and Complex Semi-Quaternions. Iran J Sci Technol Trans Sci 44, 1483–1493 (2020). https://doi.org/10.1007/s40995-020-00956-7
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DOI: https://doi.org/10.1007/s40995-020-00956-7
Keywords
- Real semi-quaternion
- Complex semi-quaternion
- Real semi-quaternion matrix
- Complex semi-quaternion matrix
- Linear real semi-quaternionic equations system
- Linear complex semi-quaternionic equations system