English

Fibonacci vector and matrix p-norms

Number Theory 2024-02-28 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2401.15972,
  title  = {Fibonacci vector and matrix p-norms},
  author = {Francisco Salas-Molina},
  journal= {arXiv preprint arXiv:2401.15972},
  year   = {2024}
}
R2 v1 2026-06-28T14:29:52.562Z