Affiliation:
1. The Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland
Abstract
Quaternions and split quaternions are used in quantum physics, computer science, and in many areas of mathematics. In this paper, we define and study two new classes of split quaternions, namely balancing split quaternions and Lucas-balancing split quaternions. Moreover, well-known properties, e.g., Catalan, d’Ocagne, and Vajda identities, for these quaternions are also presented. We give matrix generators for balancing split quaternions and Lucas-balancing split quaternions, too.
Reference34 articles.
1. Quaternions and matrices of quaternions;Zhang;Linear Algebra Appl.,1997
2. Quaternionic eiqenvalue problem;Leo;J. Math. Phys.,2002
3. Ward, J.P. (2012). Quaternions and Cayley Numbers: Algebra and Applications, Springer.
4. Generalized quaternions and their algebraic properties;Jafari;Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.,2015
5. On systems of algebra involving more than one imaginary;Cockle;Philos. Mag. III,1849
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