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Journals / Gazi University Journal of Science / 2018 / Cilt: 31 - Sayı: 2

On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number

Naim TUĞLU
Can KIZILATEŞ
Pages
555–567
Publication Date
2022-11-03
DOI
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AI Summary & Key Takeaways

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

In this paper, we study the spectral norms of the geometric circulant matrices𝑇𝑟∗ = 𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1) and the symmetric geometric circulant matrices𝑆𝑇𝑟∗ = 𝑆𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1), where 𝑇𝑛 denotes the 𝑛𝑡ℎ Tribonacci number and 𝑟 is any complex number.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the spectral norms of the geometric circulant matrices𝑇𝑟∗ = 𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1) and the symmetric geometric circulant matrices𝑆𝑇𝑟∗ = 𝑆𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1), where 𝑇𝑛 denotes the 𝑛𝑡ℎ Tribonacci number and 𝑟 is any complex number.
📊
Key Findings & Data:In this paper, we study the spectral norms of the geometric circulant matrices𝑇𝑟∗ = 𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1) and the symmetric geometric circulant matrices𝑆𝑇𝑟∗ = 𝑆𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1), where 𝑇𝑛 denotes the 𝑛𝑡ℎ Tribonacci number and 𝑟 is any complex number.
💡
Conclusion & Impact:In this paper, we study the spectral norms of the geometric circulant matrices𝑇𝑟∗ = 𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1) and the symmetric geometric circulant matrices𝑆𝑇𝑟∗ = 𝑆𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1), where 𝑇𝑛 denotes the 𝑛𝑡ℎ Tribonacci number and 𝑟 is any complex number.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we study the spectral norms of the geometric circulant matrices𝑇𝑟∗ = 𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1) and the symmetric geometric circulant matrices𝑆𝑇𝑟∗ = 𝑆𝐶𝑖𝑟𝑐𝑟∗(𝑇0, 𝑇1, ⋯ , 𝑇𝑛−1), where 𝑇𝑛 denotes the 𝑛𝑡ℎ Tribonacci number and 𝑟 is any complex number.

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Cite This Article

TUĞLU, N., KIZILATEŞ, C. (2022). On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science, Cilt: 31 - Sayı: 2, 555–567. https://ajindex.com/articles/650975

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References (16)

  1. Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 160: 125-132, (2005).
  2. Kocer, EG, Mansour, T, Tuglu, N., “Norms of circulant and semicirculant matrices with Horadam's numbers”, Ars Combinatoria, 85: 353-359, (2007).
  3. Shen, S.Q, Cen, J.M., “On the bounds for the norms of r −circulant matrices with Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 216: 2891-2897, (2010).
  4. Bahsi, M., “On the norms of r − circulant matrices with the hyperharmonic numbers”, Journal of Mathematical Inequalities, 10: (2), 445-458, (2016).
  5. Bahsi, M. and Solak, S., “On the norms of r − circulant matrices with the hyper-Fibonacci and Lucas numbers”, Journal of Mathematical Inequalities,8: (4), 693-705, (2014).
  6. Kızılateş, C. and Naim, T., “On the bounds for the spectral norms of geometric circulant matrices”, Journal of Inequalities and Applications, 2016:312 (2016).
  7. Tuglu, N. and Kızılateş C., “On the norms of circulant and r −circulant matrices with the hyperharmonic Fibonacci numbers”, Journal of Inequalities and Applications, 2015: 253, (2015).
  8. Tuglu, N, Kızılateş, C, Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Advances Difference Equations, 2015: 297, (2015).
  9. Tuglu, N. and Kızılateş, C., “On the norms of some special matrices with the harmonic Fibonacci numbers”, Gazi University Journal of Science 28: (3) 447-501, (2015).
  10. Yazlik, Y, Taskara, N., “On the norms of an r −circulant matrix with the generalized k −Horadam numbers”, Journal of Inequalities and Applications, 2013: 394, (2013).
  11. R.A. Horn, C.R. Johnson, “Matrix Analysis”, Cambridge University Press,
  12. Cambridge, UK, 1985.
  13. R.A. Horn, C.R. Johnson, “Topics in Matrix Analysis”, Cambridge University Press, 1991, 259- 260. He, C, Ma, J, Zhang, K, Wang, Z., “The upper bound estimation on the spectral norm r −circulant matrices with the Fibonacci and Lucas numbers”, Journal of Inequalities and Applications, 2015: 72, (2015).
  14. Bahsi, M., “On the norms of circulant matrices with the generalized Fibonacci and Lucas numbers”, TWWS Journal of Pure and Applied. Mathematics, 6: (1), 84-92, (2015).
  15. Jiang, Z. and Zhou, J., “A note on spectral norms of even-order r −circulant matrices”, Applied Mathematics and Computation, 250: 368-371, (2015).
  16. Sintunavarat, W., “The upper bound estimation for the spectral norm of r −circulant and symmetric r − circulant matrices with the Padovan sequence”, Journal of Nonlinear Science and its Appli