On Pell and Pell-Lucas Vectors and Their Properties.
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| Title: | On Pell and Pell-Lucas Vectors and Their Properties. |
|---|---|
| Authors: | UYSAL, Mine1 mine.uysal@erzincan.edu.tr, OZKAN, Engin2 |
| Source: | Gazi University Journal of Science. 2026, Vol. 39 Issue 1, p415-440. 26p. |
| Subjects: | Linear algebra, Recursive sequences (Mathematics), Identities (Mathematics), Mathematical sequences, Lucas numbers, Cosine function |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Gazi University Journal of Science is the property of Gazi University Journal of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194600958 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On Pell and Pell-Lucas Vectors and Their Properties. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22UYSAL%2C+Mine%22">UYSAL, Mine</searchLink><relatesTo>1</relatesTo><i> mine.uysal@erzincan.edu.tr</i><br /><searchLink fieldCode="AR" term="%22OZKAN%2C+Engin%22">OZKAN, Engin</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Gazi+University+Journal+of+Science%22">Gazi University Journal of Science</searchLink>. 2026, Vol. 39 Issue 1, p415-440. 26p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Linear+algebra%22">Linear algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+sequences+%28Mathematics%29%22">Recursive sequences (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Identities+%28Mathematics%29%22">Identities (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+sequences%22">Mathematical sequences</searchLink><br /><searchLink fieldCode="DE" term="%22Lucas+numbers%22">Lucas numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Cosine+function%22">Cosine function</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Gazi University Journal of Science is the property of Gazi University Journal of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.35378/gujs.1691819 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 26 StartPage: 415 Subjects: – SubjectFull: Linear algebra Type: general – SubjectFull: Recursive sequences (Mathematics) Type: general – SubjectFull: Identities (Mathematics) Type: general – SubjectFull: Mathematical sequences Type: general – SubjectFull: Lucas numbers Type: general – SubjectFull: Cosine function Type: general Titles: – TitleFull: On Pell and Pell-Lucas Vectors and Their Properties. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: UYSAL, Mine – PersonEntity: Name: NameFull: OZKAN, Engin IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13039709 Numbering: – Type: volume Value: 39 – Type: issue Value: 1 Titles: – TitleFull: Gazi University Journal of Science Type: main |
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