**Samet Arpacı and Fatih Yılmaz**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 1, Pages 34–46

DOI: 10.7546/nntdm.2024.30.1.34-46

**Full paper (PDF, 316 Kb)**

## Details

### Authors and affiliations

Samet Arpacı

*Department of Mathematics, University of Ankara Hacı Bayram Veli
Ankara, 69000, Turkey*

Fatih Yılmaz

*Department of Mathematics, University of Ankara Hacı Bayram Veli
Ankara, 69000, Turkey*

### Abstract

In this study, by the motivation of the papers in the literature, we construct a special geometric circulant matrix whose entries are the Leonardo numbers. Then, we investigate some linear algebraic properties of these matrices. More specifically, we present some bounds for the spectral norm, as well as Euclidean norm of this matrix form. For this purpose, we benefit from the spectacular properties of the Leonardo numbers. Furthermore, we throw light on the obtained results with examples. In addition to all these, we give two Matlab code in order to calculate the results related norms more easily and more accurately in a short time in the computer environment.

### Keywords

- Circulant matrices
- Geometric circulant matrices
- Leonardo numbers
- Matrix norm
- Spectral norm

### 2020 Mathematics Subject Classification

- 11B83
- 11B37
- 05A15

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### Manuscript history

- Received: 15 August 2023
- Revised: 13 January 2024
- Accepted: 22 February 2024
- Online First: 26 February 2024

### Copyright information

Ⓒ 2024 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).

## Related papers

- Shannon, A. G. (2019). A note on generalized Leonardo numbers.
*Notes on Number Theory and Discrete Mathematics*, 25(3), 97–101.

## Cite this paper

Arpacı, S., & Yılmaz, F. (2024). Some results on geometric circulant matrices involving the Leonardo numbers. *Notes on Number Theory and Discrete Mathematics*, 30(1), 34-46, DOI: 10.7546/nntdm.2024.30.1.34-46.