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The Scientific World Journal
Volume 2014 (2014), Article ID 563181, 6 pages
http://dx.doi.org/10.1155/2014/563181
Research Article

On the Solutions of Some Linear Complex Quaternionic Equations

1Department of Mathematics, Faculty of Art and Science, Mustafa Kemal University, Tayfur Sökmen Campus, 31100 Hatay, Turkey
2Department of Mathematics, Faculty of Kamil Özdağ Science, Karamanoğlu Mehmetbey University, 70100 Karaman, Turkey

Received 22 January 2014; Accepted 11 June 2014; Published 2 July 2014

Academic Editor: José Carlos Costa

Copyright © 2014 Cennet Bolat and Ahmet İpek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some complex quaternionic equations in the type are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.