Integer Powers of Complex Tridiagonal and Anti-Tridiagonal Matrices

TL;DR

This paper derives formulas for the r-th power of certain complex tridiagonal matrices and explores factorizations of Fibonacci polynomials, contributing to matrix analysis and polynomial theory.

Contribution

It provides the general expression for powers of complex tridiagonal matrices and introduces complex factorizations of Fibonacci polynomials, a novel combination of matrix and polynomial analysis.

Findings

Explicit formulas for matrix powers derived

Complex factorizations of Fibonacci polynomials obtained

Potential applications in computational mathematics

Abstract

In this paper, we derive the general expression of the r-th power for some n-square complex tridiagonal matrices. Additionally, we obtain the complex factorizations of Fibonacci polynomials.