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SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

  • Miladinovic, Marko (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE UNIVERSITY OF NIS) ;
  • Stanimirovic, Predrag (EPARTMENT OF MATHEMATICS FACULTY OF SCIENCE UNIVERSITY OF NIS)
  • Received : 2009.02.03
  • Published : 2011.01.01

Abstract

The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ 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 $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ 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.

Keywords

generalized Fibonaci numbers;generalized Fibonaci matrix;Lucas numbers;Lucas matrix

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