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Journals / Gazi University Journal of Science / 2026 / Volume: 39 Issue: 1

On Pell and Pell-Lucas Vectors and Their Properties

Mine Uysal(Erzincan binali yıldırım)0000-0002-2362-3097
Engin Özkan(Marmara university)0000-0002-4188-7248
Pages
—
Publication Date
2026-01-30
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AI Summary & Key Takeaways

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

Finally, we derive some important identities calculated in these number sequences for these vector sequences.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we define a new application of Pell and Pell-Lucas numbers, the vectors of Pell and Pell-Lucas sequences.
📊
Key Findings & Data:We examine them in 2 and 3 dimensions, then we give the definition of generalized vectors.
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Conclusion & Impact:Finally, we derive some important identities calculated in these number sequences for these vector sequences.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Pell numbers · Pell vectors · Inner product

Abstract

In this paper, we define a new application of Pell and Pell-Lucas numbers, the vectors of Pell and Pell-Lucas sequences. We examine them in 2 and 3 dimensions, then we give the definition of generalized vectors. Then, we define these vectors as vector sequences. We analyze the properties of these vectors both as linear algebra and as a number sequence. We first investigate the vectorial properties of these generalized vectors. Then, we define these generalized vectors as a sequence of numbers and give the recurrence relation. We also calculate the cosines of the angles between these vectors. Finally, we derive some important identities calculated in these number sequences for these vector sequences.

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Cite This Article

Uysal, M., Özkan, E., *, M. U. (2026). On Pell and Pell-Lucas Vectors and Their Properties. Gazi University Journal of Science, Volume: 39 Issue: 1. https://doi.org/10.35378/gujs.1691819

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