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http://dx.doi.org/10.4134/JKMS.2011.48.1.033

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)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.1, 2011 , pp. 33-48 More about this Journal
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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