On circulant matrices with Fibonacci quaternions

Seda Yamaç Akbıyık, Fatih Yılmaz, Serhat Yıldırım, Umut Selvi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 3, Pages 624–634
DOI: 10.7546/nntdm.2025.31.3.624-634
Full paper (PDF, 241 Kb)

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Authors and affiliations

Seda Yamaç Akbıyık
Department of Electric Electronic Engineering, Istanbul Topkapı University
Istanbul, Türkiye

Fatih Yılmaz
Department of Mathematics, University of Ankara Haci Bayram Veli
Ankara, Türkiye

Serhat Yıldırım
DepaDepartment of Mathematics, University of Ankara Haci Bayram Veli
Ankara, Türkiye

Umut Selvi
Department of Mathematics, University of Ankara Haci Bayram Veli
Ankara, Türkiye

Abstract

In literature, there exist many papers that compute determinants and some kinds of norms of circulant matrices involving some well-known number sequences. In this paper, we obtain an explicit formula for the determinant of a circulant matrix involving the well-known Fibonacci quaternions. Then, we obtain the Euclidean and spectral norms of these matrices.

Keywords

• Circulant matrix
• Fibonacci quaternion
• Determinant
• Norm

2020 Mathematics Subject Classification

• 11B83
• 11B37
• 05A15

References

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Manuscript history

• Received: 5 February 2024
• Revised: 1 September 2025
• Accepted: 10 September 2025
• Online First: 16 September 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).