Cholesky Factorization of the Generalized Symmetric k- Fibonacci Matrix

Abstract

Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse factorizations of two kinds of generalized k-Fibonacci matrices. We derive some useful identities of the k-Fibonacci sequence. We investigate the Cholesky factorization of the generalized symmetric k-Fibonacci matrix by using these identities.