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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.15972 |
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| _version_ | 1866909120788955136 |
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| author | Salas-Molina, Francisco |
| author_facet | Salas-Molina, Francisco |
| contents | This paper delves into vector and matrix norms of Fibonacci numbers. Two classes of Fibonacci vectors and a parametric p-norm are defined. From this definition, several properties of Fibonacci vector and matrix p-norms are described by varying parameter p. A closed-form expression is given to obtain the value of p, setting the difference between the p-norm and the infinite norm below a given threshold. A new class of symmetric k-Fibonacci matrix is defined such that a simple reorganization simplifies the computation of its p-norm. The analysis is extended to p-distances when considering the norm of the difference of two vectors (matrices) of the same size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fibonacci vector and matrix p-norms Salas-Molina, Francisco Number Theory This paper delves into vector and matrix norms of Fibonacci numbers. Two classes of Fibonacci vectors and a parametric p-norm are defined. From this definition, several properties of Fibonacci vector and matrix p-norms are described by varying parameter p. A closed-form expression is given to obtain the value of p, setting the difference between the p-norm and the infinite norm below a given threshold. A new class of symmetric k-Fibonacci matrix is defined such that a simple reorganization simplifies the computation of its p-norm. The analysis is extended to p-distances when considering the norm of the difference of two vectors (matrices) of the same size. |
| title | Fibonacci vector and matrix p-norms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.15972 |