On linear algebra of one type of symmetric matrices with harmonic Fibonacci entries

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
Full paper (PDF, 209 Kb)

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