Moore-Penrose inverse of generalized Fibonacci matrix and its applications

摘要

Let s be arbitrary integer, we introduce the notion of the matrix U-n((a,b,s)) of type s, whose nonzero entries are the classical Horadam numbers U-n((a,b)). In this paper we consider singular case s = -1, then the Moore-Penrose inverse of the matrix U-n((a,b,-1)) is given. In the case A = B = 1, we obtain the Pseudoinverse of the generalized Fibonacci matrix F-n((a,b,-1)). In addition, correlations between the matrix U-n((a,b,-1)) and the generalized Pascal matrices are discussed, and some combinatorial identities involving the Horadam numbers are derived.