Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NOTES ON GENERALIZED FIBONACCI NUMBERS AND MATRICES

  • Received : 2021.07.08
  • Accepted : 2022.08.16
  • Published : 2022.12.25
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Abstract

In this study, some new relations between generalized Fibonacci numbers and matrices are given. The work is designed in three stages: Firstly, it is obtained a relation between generalized Fibonacci numbers and integer powers of the matrices X satisfying the relation X2 = pX +qI, and also, many results are derived from obtained relation. Then, it is established more general relation between generalized Fibonacci numbers and the square matrices X satisfying the condition X2 = VnX - (-q)nI. Finally, some applications and numerical examples related to the obtained results are given.

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References

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