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SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES
Miladinovic, Marko,Stanimirovic, Predrag Korean Mathematical Society 2011 대한수학회지 Vol.48 No.1
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.
SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES
Marko Miladinovic,Predrag Stanimirovi 대한수학회 2011 대한수학회지 Vol.48 No.1
The notion of the generalized Fibonacci matrix <수식> 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 <수식> is derived. Correlations between the matrix <수식> 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. The notion of the generalized Fibonacci matrix <수식> 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 <수식> is derived. Correlations between the matrix <수식> 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.