Mücahit Akbıyık, Seda Yamaç Akbıyık and Fatih Yılmaz

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 3, Pages 399–410

DOI: 10.7546/nntdm.2022.28.3.399-410

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## Details

### Authors and affiliations

**Mücahit Akbıyık**

*Department of Mathematics, Beykent University
Istanbul, Turkey*

**Seda Yamaç Akbıyık**

*Department of Computer Engineering, Istanbul Gelisim University
Istanbul, Turkey*

**Fatih Yılmaz**

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

### Abstract

This paper focuses on a specially constructed matrix whose entries are harmonic Fibonacci numbers and considers its Hadamard exponential matrix. A lot of admiring algebraic properties are presented for both of them. Some of them are determinant, inverse in usual and in the Hadamard sense, permanents, some norms, etc. Additionally, a MATLAB-R2016a code is given to facilitate the calculations and to further enrich the content.

### Keywords

- Harmonic Fibonacci numbers
- Norm
- Determinant
- Permanent

### 2020 Mathematics Subject Classification

- 11B39
- 15A09
- 15A15
- 65F35

### References

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### Manuscript history

- Received: 17 February 2022
- Revised: 1 July 2022
- Accepted: 8 July 2022
- Online First: 9 July 2022

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## Cite this paper

Akbıyık, M., Akbıyık, S. Y., & Yılmaz, F. (2022). On linear algebra of one type of symmetric matrices with harmonic Fibonacci entries. *Notes on Number Theory and Discrete Mathematics*, 28(3), 399-410, DOI: 10.7546/nntdm.2022.28.3.399-410.