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Journals / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

On Lucas numbers by the matrix method

Fikri KÖKEN
Durmuş BOZKURT
Pages
471–475
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study we define the Lucas $Q_L$-matrix similar to the Fibonacci Q-matrix.
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Key Findings & Data:The Lucas $Q_L$-matrix is different from the Fibonacci Q- matrix, but is related to it.
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Conclusion & Impact:Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study we define the Lucas $Q_L$-matrix similar to the Fibonacci Q-matrix. The Lucas $Q_L$-matrix is different from the Fibonacci Q- matrix, but is related to it. Using this matrix representation, we have found some well-known equalities and a Binet-like formula for the Lucas numbers.

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Cite This Article

KÖKEN, F., BOZKURT, D. (2022). On Lucas numbers by the matrix method. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 471–475. https://ajindex.com/articles/530612

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References (5)

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  2. Kalman, D. and Mena, R. The Fibonacci numbers – exposed, Math. Mag. 76, 81–167, 2003
  3. Koshy, T. Fibonacci and Lucas Numbers with Applications (Wiley - Interscience, New York, 2001)
  4. Silvester, J.R. Fibonacci properties by matrix methods, Mathematical Gazette 63, 188–191, 1979
  5. Vajda, S. Fibonacci and Lucas numbers, and the Golden Section. Theory and applications (Ellis Horwood Limited, Chichester, 1989).