On the Semisimilarity and Consemisimilarity of Split Quaternions

YILDIZ Ö. G., Kosal H. H., Tosun M.

Advances in Applied Clifford Algebras, vol.26, no.2, pp.847-859, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s00006-015-0633-y
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.847-859
  • Keywords: semiconsimilarity, semisimilarity, Split quaternion
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2015, Springer International Publishing.In this study, we introduce the concept of semisimilarity and consemisimilarity of split quaternions. Moreover, we examine the solvability conditions and general solutions of systems xay= b, ybx= aand x~ ay= b, y~ bx= a in split quaternions. If there exist x and y that satisfy first equations system, then a and b are said to be semisimilar, if there exist x and y that satisfy second equations system, then a and b are said to be consemisimilar.