The Hadamard Products for Bi-periodic Fibonacci and Bi-periodic Lucas Generating Matrices

Abstract

In this paper, firstly, we define the $Q_{q}$ \textit{-generating matrix} for bi-periodic Fibonacci polynomial. And we give $n$th power, determinant and some properties of the bi-periodic Fibonacci polynomial by considering this matrix representation. Also, we introduce the Hadamard products for bi-periodic Fibonacci $Q_{q}^{n}$ generating matrix and bi-periodic Lucas $Q_{l}^{n}$ generating matrix of which entries are bi-periodic Fibonacci and Lucas numbers. Then, we investigate some properties of these products.

Keywords

• bi-periodic Fibonacci numbers,bi-periodic Lucas numbers,Fibonacci Q matrix,matrix method,bi-periodic Fibonacci polynomial,generating matrix

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