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

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

In this paper, we study the spectral norms of the geometric circulant matrices??∗ = ?????∗(?0, ?1, ⋯ , ??−1) and the symmetric geometric circulant matrices???∗ = ??????∗(?0, ?1, ⋯ , ??−1), where ?? denotes the ??ℎ Tribonacci number and ? is any complex number.

___

  • Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation, 160: 125-132, (2005).
  • Kocer, EG, Mansour, T, Tuglu, N., “Norms of circulant and semicirculant matrices with Horadam's numbers”, Ars Combinatoria, 85: 353-359, (2007).
  • 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).
  • Bahsi, M., “On the norms of r − circulant matrices with the hyperharmonic numbers”, Journal of Mathematical Inequalities, 10: (2), 445-458, (2016).
  • 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).
  • Kızılateş, C. and Naim, T., “On the bounds for the spectral norms of geometric circulant matrices”, Journal of Inequalities and Applications, 2016:312 (2016).
  • 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).
  • Tuglu, N, Kızılateş, C, Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Advances Difference Equations, 2015: 297, (2015).
  • 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).
  • 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).
  • R.A. Horn, C.R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, UK, 1985.
  • 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).
  • 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).
  • Jiang, Z. and Zhou, J., “A note on spectral norms of even-order r −circulant matrices”, Applied Mathematics and Computation, 250: 368-371, (2015).
  • 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 Applications, 9: 92-101, (2016).
  • Li, J, Jiang, Z, Lu, F., “Determinants, Norms and spread of circulant matrices with Tribonacci and generalized Lucas numbers”, Abstract Applied Analysis, 2014, Article ID 381829 (2014).
  • Rabinowitz, S., “Algorithmic manipulation of third-order linear recurrences”, The Fibonacci Quarterly, 34: (5), 34: 447-463, (1996).
  • Tascı, D., “On quadrapell numbers and quadrapell polynomials”, Hacettepe Journal of Mathematics and Statistics, 38: (3), 265-275, (2009).