# Bi-periodic Fibonacci matrix polynomial and its binomial transforms

## TL;DR

This paper introduces a new matrix polynomial based on bi-periodic Fibonacci matrices, explores its properties, and examines its binomial transforms, contributing to the mathematical understanding of Fibonacci-related matrix polynomials.

## Contribution

It presents a novel bi-periodic Fibonacci matrix polynomial and analyzes its properties and binomial transforms, expanding the theoretical framework of Fibonacci matrix polynomials.

## Key findings

- Derived properties of the bi-periodic Fibonacci matrix polynomial
- Established binomial transform formulas for the new matrix polynomial
- Enhanced understanding of Fibonacci matrix polynomial structures

## Abstract

In this paper, we consider the matrix polynomial obtained by using bi-periodic Fibonacci matrix polynomial. Then, we give some properties and binomial transforms of the new matrix polynomials.