On some 3 × 3 dimensional matrices associated with generalized Fibonacci numbers

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
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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.

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