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The generalized Lilbert matrix

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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.

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Authors and Affiliations

  1. TOBB University of Economics and Technology Mathematics Department, 06560, Ankara, Turkey

    Emrah Kılıç & Helmut Prodinger

  2. Department of Mathematics, University of Stellenbosch, Stellenbosch, 7602, South Africa

    Emrah Kılıç & Helmut Prodinger

Authors
  1. Emrah Kılıç
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  2. Helmut Prodinger
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Correspondence to Emrah Kılıç.

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Kılıç, E., Prodinger, H. The generalized Lilbert matrix. Period Math Hung 73, 62–72 (2016). https://doi.org/10.1007/s10998-016-0128-1

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  • DOI: https://doi.org/10.1007/s10998-016-0128-1

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