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

Yıl 2018, Cilt: 6 Sayı: 1, 12 - 18, 27.04.2018

Arzu Coskun Necati Taskara

https://doi.org/10.36753/mathenot.421748

Cited By: 2

Öz

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.

Anahtar Kelimeler

Third order linear recurrent sequence, Cordonnier numbers, Perrin numbers, Van Der Laan numbers, circulant matrix

Kaynakça

• [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.