On Pell and Pell-Lucas Vectors and Their Properties

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Uysal M., Özkan E.

GAZI UNIVERSITY JOURNAL OF SCIENCE, cilt.39, sa.Advanced Online Publication, ss.415-440, 2026 (ESCI, Scopus, TRDizin)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 39 Sayı: Advanced Online Publication
• Basım Tarihi: 2026
• Doi Numarası: 10.35378/gujs.1691819
• Dergi Adı: GAZI UNIVERSITY JOURNAL OF SCIENCE
• Derginin Tarandığı İndeksler: Scopus, Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.415-440
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Marmara Üniversitesi Adresli: Evet

Özet

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.