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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis:The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters.
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Key Findings & Data:Explicit formulae are derived for the $LU$-decomposition and their inverses, as well as the Cholesky decomposition.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Determinant · inverse matrix · $LU$ factorization
Abstract
The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae 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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Cite This Article
KILIÇ, E., ARIKAN, T. (2022). The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics, Cilt: 40 - Sayı: 5, 960–972. https://ajindex.com/articles/608037