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

Authors : Arzu COŞKUN, Necati TAŞKARA

Pages : 272-278

View : 14 | Download : 6

Publication Date : 2018-10-15

Article Type : Research Paper

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