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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

Linear algebra of the Lucas matrix

Nurettin Irmak(NIGDE UNIVERSITY)0000-0003-0409-4342
Cahit Köme(NEVSEHIR HACI BEKTAS VELI UNIVERSITY)0000-0002-6488-9035
Pages
—
Publication Date
2021-04-11
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we obtain the upper and lower bounds for the eigenvalues of the symmetric Lucas matrix by using some majorization techniques.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we give the factorizations of the Lucas and inverse Lucas matrices.
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Key Findings & Data:We also investigate the Cholesky factorization of the symmetric Lucas matrix.
💡
Conclusion & Impact:Moreover, we obtain the upper and lower bounds for the eigenvalues of the symmetric Lucas matrix by using some majorization techniques.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lucas Matrix · Cholesky factorization · eigenvalues

Abstract

In this paper, we give the factorizations of the Lucas and inverse Lucas matrices. We also investigate the Cholesky factorization of the symmetric Lucas matrix. Moreover, we obtain the upper and lower bounds for the eigenvalues of the symmetric Lucas matrix by using some majorization techniques.

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Cite This Article

Irmak, N., Köme, C. (2021). Linear algebra of the Lucas matrix. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.746184

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References (11)

  1. C.M. Fonseca and E. Kılıç, An observation on the determinant of a Sylvester-Kac type matrix, An. Univ. "Ovidius" Constanta Ser. Mat. 28 (1), 111–115, 2020.
  2. C.M. Fonseca and Kılıç, A new type of Sylvester–Kac matrix and its spectrum, https://doi.org/10.1080/03081087.2019.1620673.
  3. G.H. Hardy, J.E. Littlewood and G. Pólya, Some simple inequalities satisfied by con- vex functions, Messenger Math. 58, 145–152, 1929.
  4. C.R. Johnson and R.A. Horn, Matrix analysis, Cambridge University Press Cam- bridge, 1985.
  5. E. Kilic and D. Tasci, The linear algebra of the Pell matrix, Bol. Soc. Mat. Mex. 11 (3), 163–174, 2005.
  6. T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, 2001.
  7. G.-Y. Lee, J.-S. Kim and S.-G. Lee, Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart. 40 (3), 203–211, 2002.
  8. G.-Y. Lee and J.-S. Kim, The linear algebra of the k−Fibonacci matrix, Linear Algebra Appl. 373, 75–87, 2003.
  9. A.W. Marshall, I. Olkin and B.C. Arnold, Inequalities: theory of majorization and its applications 143, Springer, 1979.
  10. P. Stanica, Cholesky factorizations of matrices associated with r−order recurrent se- quences, Integers, 5 (2), A16, 2005.
  11. Z. Zhang and Y. Zhang, The Lucas matrix and some combinatorial identities, Indian J. Pure Appl. Math. 38 (5), 457–465, 2007.