Multicomponent hybrid numbers: On algebraic properties and matrix representations of hybrid-hyperbolic numbers

Bahar Doğan Yazıcı and Murat Tosun
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 26—40
DOI: 10.7546/nntdm.2022.28.1.26-40
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Authors and affiliations

Bahar Doğan Yazıcı
Department of Mathematics, Bilecik Seyh Edebali University
11200, Bilecik, Turkey

Murat Tosun
Department of Mathematics, Sakarya University
54050, Sakarya, Turkey

Manuscript history

  • Received: 29 January 2021
  • Revised: 22 December 2022
  • Accepted: 18 January 2022
  • Online First: 7 February 2022

Abstract

In this study, the hybrid-hyperbolic numbers are introduced. This number system is a more general form of the hybrid number system, which is an interesting number system, as well as a number system that includes multicomponent number systems (i.e., complex-hyperbolic, dual-hyperbolic and bihyperbolic numbers). In this paper, we give algebraic properties of hybrid-hyperbolic numbers. In addition, 2 × 2 and 4 × 4 hyperbolic matrix representations of hybrid-hyperbolic numbers are given and some properties of them are examined.

Keywords

  • Hybrid numbers
  • Complex-hyperbolic numbers
  • Dual-hyperbolic numbers
  • Bihyperbolic numbers
  • Hybrid-hyperbolic numbers

2020 Mathematics Subject Classification

  • 13A18
  • 53A17

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Cite this paper

Doğan Yazıcı, B., & Tosun, M. (2022). Multicomponent hybrid numbers: On algebraic properties and matrix representations of hybrid-hyperbolic numbers. Notes on Number Theory and Discrete Mathematics, 28(1), 26-40, DOI: 10.7546/nntdm.2022.28.1.26-40.

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