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
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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.
- Harmonic Fibonacci numbers
2020 Mathematics Subject Classification
- Bahsi, M., & Solak, S. (2010). On the matrices with Harmonic numbers. Gazi Journal of Science, 23(4), 445–448.
- Bapat, R. B. (1988). Multinomial probabilities, permanents and a conjecture of Karlin and Rmou. Proceedings of the American Mathematical Society, 102(3), 467–472.
- Bozkurt, D. (2011). A note on the spectral norms of the matrices connected integer numbers sequence. arXiv. Available online at: https://arxiv.org/abs/1105.1724v1
- Brualdi, R. A., Gibson, P.M. (1977). Convex polyhedra of doubly stochastic matrices. I. Applications of the permanent function. Journal of Combinatorial Theory, Series A, 22, 194–230.
- Graham, R., Knuth, D., & Patashnik, K. (1989). Concrete Mathematics. Addison-Wesley, Reading.
- Ipek, A., & Akbulak, M. (2012). Hadamard exponential Hankel Matrix, its eigenvalues and some norms. Mathematical Sciences Letters, 1, 81–87.
- Jafari Petrudi, S. H., & Pirouz, B. (2015). A particular matrix, its inversion and some norms. Applied and Computational Mathematics, 4(2), 47–52.
- Reams, R. (1999). Hadamard inverses, square roots and products of almost semidefinite matrices. Linear Algebra and Its Applications, 288, 35–43.
- Solak, S., & Bahsi, M. (2013). On the spectral norms of Toeplitz matrices with Fibonacci and Lucas numbers, Nonlinear Analysis. Hacettepe Journal of Mathematics and Statistics, 42(1), 15–19.
- Tuglu, N., & Kızılates, C. (2015). On the Norms of Some Special Matrices with the Harmonic Fibonacci Numbers. Gazi University Journal of Science, 28(3), 497–501.
- Tuglu, N., Kızılates, C., & Kesim, S. (2015). On the harmonic and hyperharmonic Fibonacci numbers. Advances in Difference Equations, 1–12.
- Yılmaz, F., & Bozkurt, D. (2011). Hessenberg matrices and the Pell and Perrin numbers. Journal of Number Theory, 131, 1390–1396.
- Zhang, F. (1999). Matrix Theory: Basic Results and Techniques. Springer-Verlag, New York..
- Received: 17 February 2022
- Revised: 1 July 2022
- Accepted: 8 July 2022
- Online First: 9 July 2022
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.