Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 795175, 6 pages
http://dx.doi.org/10.1155/2014/795175
Research Article

On the Spectrum and Spectral Norms of -Circulant Matrices with Generalized -Horadam Numbers Entries

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 17 May 2014; Accepted 25 August 2014; Published 31 August 2014

Academic Editor: Chengpeng Bi

Copyright © 2014 Lele Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Solak, “On the norms of circulant matrices with the Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 160, no. 1, pp. 125–132, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  2. A. İpek, “On the spectral norms of circulant matrices with classical Fibonacci and Lucas numbers entries,” Applied Mathematics and Computation, vol. 217, no. 12, pp. 6011–6012, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. W. Bani-Domi and F. Kittaneh, “Norm equalities and inequalities for operator matrices,” Linear Algebra and Its Applications, vol. 429, no. 1, pp. 57–67, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Shen and J. Cen, “On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 2891–2897, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. S. Shen and J. Cen, “On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 9–12, pp. 569–578, 2010. View at Google Scholar · View at MathSciNet
  6. Y. Yazlik and N. Taskara, “A note on generalized k-Horadam sequence,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 36–41, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. Yazlik and N. Taskara, “On the norms of an r-circulant matrix with the generalized k-Horadam numbers,” Journal of Inequalities and Applications, vol. 2013, article 394, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Y. Yazlik and N. Taskara, “Spectral norm, eigenvalues and determinant of circulant matrix involving the generalized k-Horadam numbers,” Ars Combinatoria, vol. 104, pp. 505–512, 2012. View at Google Scholar · View at Scopus
  9. Z. Jiang and Z. Zhou, “Nonsingularity of r-circulant matrices,” Applied Mathematics: A Journal of Chinese Universities, vol. 10, no. 2, pp. 222–226, 1995. View at Google Scholar · View at MathSciNet
  10. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985. View at Publisher · View at Google Scholar · View at MathSciNet
  11. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 3rd edition, 1976. View at MathSciNet
  12. E. G. Kocer, T. Mansour, and N. Tuglu, “Norms of circulant and semicirculant matrices with Horadam's numbers,” Ars Combinatoria, vol. 85, pp. 353–359, 2007. View at Google Scholar · View at MathSciNet · View at Scopus