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.