Hyper-Number Generalized Quaternions

ALAGÖZ Y., Özyurt G.

Computational Mathematics and Mathematical Physics, cilt.64, sa.5, ss.908-917, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 5
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1134/s0965542524700337
  • Dergi Adı: Computational Mathematics and Mathematical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, INSPEC, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.908-917
  • Anahtar Kelimeler: generalized quaternion, hyper-number, hyper-number generalized quaternion
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Abstract: The main aim of this paper is to introduce generalized quaternions with hyper-number coefficients. For this, firstly, a new number system is defined, which is the generalization of bicomplex numbers, hyper-double numbers and hyper-dual numbers. And any element of this generalization is called a hyper-number. Then, real matrix representation and vector representation of a hyper-number are given. Secondly, hyper-number generalized quaternions and their algebraic properties are introduced. For a hyper-number generalized quaternion, real generalized quaternion matrix representation is presented. Next, because of lack of commutativity, for a hyper-number generalized quaternion, two different hyper-number matrix representations are calculated. Moreover, real matrix representations of a hyper-number generalized quaternion is expressed by matrix representation of a hyper-number. Finally, vector representations of a hyper-number generalized quaternion are given and properties of this representations are investigated.