Factorizations and eigenvalues of the \((r, k)\)-bonacci matrices

DOI10.1007/s40314-023-02331-9zbMath1524.11068OpenAlexW4377195879MaRDI QIDQ6103375

Cahit Köme

Publication date: 2 June 2023

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-023-02331-9

zbMATH Keywords

eigenvaluesCholesky factorizationmajorization\((r, k)\)-bonacci matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Inequalities involving eigenvalues and eigenvectors (15A42) Matrices of integers (15B36) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Matrices, determinants in number theory (11C20)

Cites Work

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• A note on generalized \(k\)-Horadam sequence
• \(k\)-step sum and \(m\)-step gap Fibonacci sequence
• Theory of Binet formulas for Fibonacci and Lucas \(p\)-numbers
• Some combinatorial identities via Fibonacci numbers
• The linear algebra of the \(k\)-Fibonacci matrix.
• The Binet formula, sums and representations of generalized Fibonacci \(p\)-numbers
• A factorization of the symmetric Pascal matrix involving the Fibonacci matrix
• On the generalized order-\(k\) Fibonacci and Lucas numbers
• The Golden Shofar
• The linear algebra of the Pell matrix
• The \(k\)-Fibonacci sequence and the Pascal 2-triangle
• Matrix Analysis
• Some combinatorial identities via k-order Fibonacci matrices
• Linear algebra of the Lucas matrix
• Inequalities: theory of majorization and its applications

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