Halim Özdemir, Sinan Karakaya and Tuğba Petik

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 3, Pages 63–72

DOI: 10.7546/nntdm.2021.27.3.63-72

**Full paper (PDF, 209 Kb)**

## Details

### Authors and affiliations

Halim Özdemir

*Department of Mathematics, University of Sakarya,
54187, Serdivan, Sakarya, Turkey*

Sinan Karakaya

*Department of Mathematics, University of Sakarya,
54187, Serdivan, Sakarya, Turkey*

Tuğba Petik

*Department of Mathematics, University of Sakarya,
54187, Serdivan, Sakarya, Turkey
*

### Abstract

In this work, it is presented a procedure to find some 3 × 3 dimensional matrices whose integer powers can be characterized by generalized Fibonacci numbers. Moreover, some numerical examples are given to exemplify the procedure established.

### Keywords

- Fibonacci numbers
- Generalized Fibonacci numbers
- Fibonacci
*Q*-matrix - Eigenvalue
- Eigenvector
- Matrix equation

### 2020 Mathematics Subject Classification

- 11B39
- 15A24

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## Cite this paper

Özdemir, H., Karakaya S., & Petik T. (2021). On some 3 × 3 dimensional matrices associated with generalized Fibonacci numbers. *Notes on Number Theory and Discrete Mathematics*, 27(3), 63-72, DOI: 10.7546/nntdm.2021.27.3.63-72.