Dergiler / Mathematical Sciences and Applications E-Notes / 2018 / Cilt: 6 - Sayı: 1

On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences

Sayfa
12–18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Consequently, by using properties of this sequence, we obtain the eigenvalues, norms and determinants of circulant matrices with Cordonnier, Perrin and Van Der Laan numbers.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers.
📊
Temel Bulgular & Veri:After, we define the circulant matrices C(Z) which entries are third order linear recurrent sequences.
💡
Sonuç & Katkı:Consequently, by using properties of this sequence, we obtain the eigenvalues, norms and determinants of circulant matrices with Cordonnier, Perrin and Van Der Laan numbers.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Third order linear recurrent sequence · Cordonnier numbers · Perrin numbers

Abstract

In this paper, firstly, we give the some fundamental properties of Van Der Laan numbers. After, we define the circulant matrices C(Z) which entries are third order linear recurrent sequences. In addition, we compute eigenvalues, spectral norm and determinant of this matrix. Consequently, by using properties of this sequence, we obtain the eigenvalues, norms and determinants of circulant matrices with Cordonnier, Perrin and Van Der Laan numbers.

🔖

Bu Makaleye Atıf Yap

COŞKUN, A., TAŞKARA, N. (2018). On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Mathematical Sciences and Applications E-Notes, Cilt: 6 - Sayı: 1, 12–18. https://ajindex.com/articles/283504

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (13)

  1. Bozkurt, D. and Dafonseca, C.M., The determinants of circulant and skew-circulant matrices with tribonacci numbers, Mathematical Sciences and Applications E-Notes 2 (2014), no. 2
  2. Bozkurt, D. and Tam, T.Y., Determinants and inverses of circulant matrices with the Jacobsthal and JacobsthalLucas numbers, Applied Mathematics and Computation 219 (2012), no.2, 544-551
  3. Davis, P. J., Circulant Matrices, John Wiley&Sons, New York, 1979
  4. Elia, M., Derived Sequences, the Tribonacci Recurrence and Cubic Forms, The Fibonacci Quarterly 37 (2001), 107-115
  5. Horn, R. A. and Johnson, C. R., Matrix Analysis, Cambridge University Press, 1985
  6. Ipek, A., On the spectral norms of circulant matrices with classical Fibonacci and Lucas numbers entries. Applied Mathematics and Computation 217 (2011), no. 12, 6011-6012
  7. Kocer, E.G., Circulant, negacyclic and semicirculant matrices with the modified Pell, Jacobsthal and JacobsthalLucas numbers, Hacettepe J. Math., and Statistics 36 (2007), no. 2, 133-142
  8. Shanon, A.G., Horadam, A.F. and Anderson, P.G., Properties of Cordonnier, Perrin and Van Der Laan numbers, International Journal of Mathematical Education in Science and Technology 37 (2006), no. 7, 825-831
  9. Shen, S.Q. and Cen, J.M., On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation 216 (2010), 2891-2897
  10. Shen, S.Q. and Cen, J.M., On the determinants and inverses of circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation 217 (2011), 9790-9797
  11. Solak, S., On the norms of circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation 160 (2005), 125-132
  12. Yazlik, Y. and Taskara, N., On the norms of an r-circulant matrix with the generalized k-Horadam numbers, Journal of Inequalities and Applications 394 (2013), 505-512
  13. Yazlik, Y. and Taskara, N., Spectral norm, eigenvalues and determinant of circulant matrix involving the generalized k-Horadam numbers, Ars Combinatoria 104 (2012), 505-512.