The k-Fibonacci matrix and the Pascal matrix

• Autorzy: Sergio Falcon
• Języki publikacji: EN

Abstrakty

EN

We define the k-Fibonacci matrix as an extension of the classical Fibonacci matrix and relationed with the k-Fibonacci numbers. Then we give two factorizations of the Pascal matrix involving the k-Fibonacci matrix and two new matrices, L and R. As a consequence we find some combinatorial formulas involving the k-Fibonacci numbers.

Słowa kluczowe

EN

Pascal matrix; k-Fibonacci numbers; Factorization of a matrix

Kategorie tematyczne

• 11B39: Fibonacci and Lucas numbers and polynomials and generalizations
• 11C20: Matrices, determinants

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1403-1410

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Sergio Falcon

• University of Las Palmas de Gran Canaria

Bibliografia

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• [8] Lee G.-Y., Kim J.-S., Lee S.-G., Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart., 2002, 40(3), 203–211
• [9] Lee G.-Y., Lee S.-G., Shin H.-G., On the k-generalized Fibonacci matrix Q k, Linear Algebra Appl., 1997, 251, 73–88 http://dx.doi.org/10.1016/0024-3795(95)00553-6
• [10] Peart P., Woodson L., Triple factorization of some Riordan matrices, Fibonacci Quart., 1993, 31(2), 121–128
• [11] Zhang Z., The linear algebra of the generalized Pascal matrix, Linear Algebra Appl., 1997, 250, 51–60 http://dx.doi.org/10.1016/0024-3795(95)00452-1
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Identyfikatory

DOI

10.2478/s11533-011-0089-9