SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

Title & Authors
SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

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