Binary matrices of order 3 associated with the Pell sequence
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912659468713984 |
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| author | Martinez, Wilson Arley Ceron, Samin Ingrid |
| author_facet | Martinez, Wilson Arley Ceron, Samin Ingrid |
| contents | In this paper, we construct Pell matrices, analogous to Fibonacci matrices, to study algebraic properties of Pell numbers via linear algebra. This framework yields identities involving the trace, inverse, and determinant, as well as matrix products that generate recurrence relations and closed-form expressions. Additionally, we classify all binary 3x3 matrices that generate the Pell equation through conjugation, providing a complete characterization of such matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16934 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Binary matrices of order 3 associated with the Pell sequence Martinez, Wilson Arley Ceron, Samin Ingrid Number Theory In this paper, we construct Pell matrices, analogous to Fibonacci matrices, to study algebraic properties of Pell numbers via linear algebra. This framework yields identities involving the trace, inverse, and determinant, as well as matrix products that generate recurrence relations and closed-form expressions. Additionally, we classify all binary 3x3 matrices that generate the Pell equation through conjugation, providing a complete characterization of such matrices. |
| title | Binary matrices of order 3 associated with the Pell sequence |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.16934 |