Similarity and consimilarity of hyper-dual generalized quaternions

ALAGÖZ Y., Özyurt G.

Mathematical Methods in the Applied Sciences, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1002/mma.10488
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: 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
  • Anahtar Kelimeler: coneigenvalue, coneigenvector, hyper-dual generalized quaternion, i-consimilarity, j-consimilarity, k-consimilarity, similarity
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

The aim of this paper is to investigate similarity and consimilarity of hyper-dual generalized quaternions and their matrices. For this purpose, we give different conjugates according to the generalized quaternionic units (Formula presented.). We present (Formula presented.) -consimilarity of hyper-dual generalized quaternions and their matrices except hyper-dual (Formula presented.) -quaternions. For the generalization consisting of hyper-dual coefficients quaternion and split quaternion, we search (Formula presented.) -consimilarity and (Formula presented.) -consimilarity with the help of (Formula presented.) -conjugate and (Formula presented.) -conjugate. We also give (Formula presented.) -coneigenvalues and (Formula presented.) -coneigenvectors of the matrices of these generalizations. In addition, we examine right coneigenvalue problem in generalized quaternion matrices for real and split quaternions. The complex matrix representation obtained through the complex adjoint matrix representation of this generalization is introduced, and its properties are presented. Besides, we give algebraic methods for the concept of right coneigenvalues and coneigenvectors for matrices, which are the generalization of real quaternion and split quaternion.