Research Article
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Year 2018, Volume: 6 Issue: 1, 12 - 18, 27.04.2018
https://doi.org/10.36753/mathenot.421748

Abstract

References

  • [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.

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

Year 2018, Volume: 6 Issue: 1, 12 - 18, 27.04.2018
https://doi.org/10.36753/mathenot.421748

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.

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Arzu Coskun This is me

Necati Taskara

Publication Date April 27, 2018
Submission Date March 26, 2016
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Coskun, A., & Taskara, N. (2018). On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Mathematical Sciences and Applications E-Notes, 6(1), 12-18. https://doi.org/10.36753/mathenot.421748
AMA Coskun A, Taskara N. On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Math. Sci. Appl. E-Notes. April 2018;6(1):12-18. doi:10.36753/mathenot.421748
Chicago Coskun, Arzu, and Necati Taskara. “On the Some Properties of Circulant Matrices With Third Order Linear Recurrent Sequences”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 12-18. https://doi.org/10.36753/mathenot.421748.
EndNote Coskun A, Taskara N (April 1, 2018) On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Mathematical Sciences and Applications E-Notes 6 1 12–18.
IEEE A. Coskun and N. Taskara, “On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 12–18, 2018, doi: 10.36753/mathenot.421748.
ISNAD Coskun, Arzu - Taskara, Necati. “On the Some Properties of Circulant Matrices With Third Order Linear Recurrent Sequences”. Mathematical Sciences and Applications E-Notes 6/1 (April 2018), 12-18. https://doi.org/10.36753/mathenot.421748.
JAMA Coskun A, Taskara N. On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Math. Sci. Appl. E-Notes. 2018;6:12–18.
MLA Coskun, Arzu and Necati Taskara. “On the Some Properties of Circulant Matrices With Third Order Linear Recurrent Sequences”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, 2018, pp. 12-18, doi:10.36753/mathenot.421748.
Vancouver Coskun A, Taskara N. On the Some Properties of Circulant Matrices with Third Order Linear Recurrent Sequences. Math. Sci. Appl. E-Notes. 2018;6(1):12-8.

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