SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

Abstract. The notion of the generalized Fibonacci matrix F(a;b;s)n of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = 1. Pseudoinverse of the generalized Fibonacci matrix F(a;b;1)n is derived. Correlations between the matrix F(a;b;1)n and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section. 1