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Periodica Mathematica Hungarica

, Volume 73, Issue 1, pp 62–72 | Cite as

The generalized Lilbert matrix

  • Emrah KılıçEmail author
  • Helmut Prodinger
Article

Abstract

We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm.

Keywords

Lilbert matrix Filbert matrix Pilbert matrix  Fibonacci numbers q-Analogues LU-decomposition Cholesky decomposition Zeilberger’s algorithm 

Mathematics Subject Classification

11B39 15B05 15A23 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.TOBB University of Economics and Technology Mathematics DepartmentAnkaraTurkey
  2. 2.Department of MathematicsUniversity of StellenboschStellenboschSouth Africa

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