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arXiv · 2401.15972

Fibonacci vector and matrix p-norms

Francisco Salas-Molina
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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.

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Francisco Salas-Molina. 2024-01-29. Fibonacci vector and matrix p-norms. https://arxiv.org/abs/2401.15972

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