Generalized $F$-Nomial Matrix and Factorizations

Abstract

In this study, we define the generalized $k$-order Fibonacci matrix and the $n\times n$ generalized Pascal matrix ${\mathcal{F}}_n(GF)$ associated with generalized $\mathcal{F}$-nomial coefficients. We find the inverse of the generalized Pascal matrix ${\mathcal{F}}_n(GF)$ associated with generalized $\mathcal{F}$-nomial coefficients. In the last section, we factorize this matrix via the generalized $k$-order Fibonacci matrix and give illustrative examples for these factorizations.