Lucas, Fibonacci, and Chebyshev polynomials from matrices

TL;DR

This paper introduces a straightforward matrix-based approach to generate Fibonacci, Lucas, Chebyshev, and Dixon polynomials using matrix powers and symmetric tensor powers.

Contribution

It provides a novel matrix formulation that simplifies the computation and understanding of these classical polynomial sequences.

Findings

Matrix formulation effectively generates polynomial sequences

Simplifies computation of polynomial powers

Connects polynomial sequences with matrix algebra

Abstract

A simple matrix formulation of the Fibonacci, Lucas, Chebyshev, and Dixon polynomials polynomials is presented. It utilizes the powers and the symmetric tensor powers of a certain matrix.