Similarity of hybrid numbers


Ozturk I., ÖZDEMİR M.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.43, no.15, pp.8867-8881, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 15
  • Publication Date: 2020
  • Doi Number: 10.1002/mma.6580
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.8867-8881
  • Keywords: double numbers, dual numbers, hybrid numbers, split quaternion, SPLIT QUATERNIONS, SEMISIMILARITY, CONSIMILARITY, MATRICES, ROOTS
  • Akdeniz University Affiliated: Yes

Abstract

The set of hybrid numbers & x1d542;& xdd42;is a noncommutative number system that unified and generalized the complex, dual, and double (hyperbolic) numbers with the relationih =-hi=epsilon+i.Two hybrid numberspandqare said to be similar if there exist a nonlightlike hybrid numberxsatisfying the equalityx(-1)qx=p. And, it is denoted byp similar to q. In this paper, we study the concept of similarity for hybrid numbers by solving the linear equationspx=xqandqx-xp=cforp,q,c is an element of & x1d542;& xdd42;.