In this study, we show that the elliptic biquaternion algebra is algebraically isomorphic to the $2\times 2$ total elliptic matrix algebra and so, we get a faithful $2\times 2$ elliptic matrix representation of an elliptic biquaternion. Also, we investigate the similarity and the MoorePenrose inverses of elliptic biquaternions by means of these matrix representations. Moreover, we establish universal similarity factorization equality (USFE) over the elliptic biquaternion algebra which reveals a deeper relationship between an elliptic biquaternion and its elliptic matrix representation. This equality and these representations can serve as useful tools for discussing many problems concerned with the elliptic biquaternions, especially for solving various elliptic biquaternion equations.
Primary Language  en 

Subjects  Engineering 
Journal Section  Articles 
Authors 

Dates 
Publication Date: December 14, 2018 
Bibtex  @conference paper { cpost479295,
journal = {Conference Proceedings of Science and Technology},
issn = {2651544X},
address = {Murat TOSUN},
year = {2018},
volume = {1 (2018)},
pages = {20  27},
doi = {},
title = {Further Results for Elliptic Biquaternions},
key = {cite},
author = {Özen, Kahraman Esen and Tosun, Murat}
} 
APA  Özen, K , Tosun, M . (2018). Further Results for Elliptic Biquaternions. Conference Proceedings of Science and Technology, 1 (2018) (1), 2027. Retrieved from http://dergipark.org.tr/cpost/issue/41126/479295 
MLA  Özen, K , Tosun, M . "Further Results for Elliptic Biquaternions". Conference Proceedings of Science and Technology 1 (2018) (2018): 2027 <http://dergipark.org.tr/cpost/issue/41126/479295> 
Chicago  Özen, K , Tosun, M . "Further Results for Elliptic Biquaternions". Conference Proceedings of Science and Technology 1 (2018) (2018): 2027 
RIS  TY  JOUR T1  Further Results for Elliptic Biquaternions AU  Kahraman Esen Özen , Murat Tosun Y1  2018 PY  2018 N1  DO  T2  Conference Proceedings of Science and Technology JF  Journal JO  JOR SP  20 EP  27 VL  1 (2018) IS  1 SN  2651544X M3  UR  Y2  2018 ER  
EndNote  %0 Conference Proceedings of Science and Technology Further Results for Elliptic Biquaternions %A Kahraman Esen Özen , Murat Tosun %T Further Results for Elliptic Biquaternions %D 2018 %J Conference Proceedings of Science and Technology %P 2651544X %V 1 (2018) %N 1 %R %U 
ISNAD  Özen, Kahraman Esen , Tosun, Murat . "Further Results for Elliptic Biquaternions". Conference Proceedings of Science and Technology 1 (2018) / 1 (December 2018): 2027. 
AMA  Özen K , Tosun M . Further Results for Elliptic Biquaternions. Conference Proceedings of Science and Technology. 2018; 1 (2018)(1): 2027. 
Vancouver  Özen K , Tosun M . Further Results for Elliptic Biquaternions. Conference Proceedings of Science and Technology. 2018; 1 (2018)(1): 2720. 