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Some results on Horadam quaternions

Author

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  • Tan, Elif
  • Leung, Ho-Hon

Abstract

In this work, we present some matrix representations associated with the Horadam quaternions which are defined by Wn=wn+wn+1i+wn+2j+wn+3k, where the components are taken from the Horadam sequence {wn}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.

Suggested Citation

  • Tan, Elif & Leung, Ho-Hon, 2020. "Some results on Horadam quaternions," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030360x
    DOI: 10.1016/j.chaos.2020.109961
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    Cited by:

    1. Pucanović, Zoran & Pešović, Marko, 2023. "Chebyshev polynomials and r-circulant matrices," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    2. Nazlıhan Terzioğlu & Can Kızılateş & Wei-Shih Du, 2022. "New Properties and Identities for Fibonacci Finite Operator Quaternions," Mathematics, MDPI, vol. 10(10), pages 1-13, May.

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