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On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers

Year 2015, Volume: 28 Issue: 3, 497 - 501, 28.05.2015

Naim Tuglu , Can Kızılateş

Abstract

The aim of this paper is to study norms of some circulant matrices and some special matrices which entries consist of harmonic Fibonacci numbers.

Keywords

Harmonic Fibonacci number Circulant Matrix Matrix norm

References

  • N. Tuglu, C. Kızılates¸, S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, ArXiv:1505.04284v1.
  • S. Solak, On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput. 160 (2005) 125–132.
  • E.G.Kocer, T. Mansour, N. Tuglu, Norms of Circulant and Semicirculant Matrices with Horadams Numbers, Ars Combinatoria, 85 (2007) 353-359.
  • S. Shen, On the norms of Toeplitz matrices involving k-Fibonacci and k-Lucas numbers, Int. J. Cont. Math. Sci. 7 (2012), 363–368.
  • M. Bahsi, S. Solak, On the matrices with Harmonic numbers, Gazi University J.Science 23 (4),(2010), 445-448.
  • J. Zhou, X. Chen, Z. Jiang, The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers, Math. Probl. Eng.Article ID 672398, 5 (2014).
  • R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
  • R.Graham, D. Knuth, K. Patashnik, Concrete Mathematics, Addison Wesley, 1989.
  • R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.

On the Norms of Some Special Matrices with the Harmonic

Year 2015, Volume: 28 Issue: 3, 497 - 501, 28.05.2015

Naim Tuglu , Can Kızılateş

Abstract

References

  • N. Tuglu, C. Kızılates¸, S. Kesim, On the harmonic and hyperharmonic Fibonacci numbers, ArXiv:1505.04284v1.
  • S. Solak, On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput. 160 (2005) 125–132.
  • E.G.Kocer, T. Mansour, N. Tuglu, Norms of Circulant and Semicirculant Matrices with Horadams Numbers, Ars Combinatoria, 85 (2007) 353-359.
  • S. Shen, On the norms of Toeplitz matrices involving k-Fibonacci and k-Lucas numbers, Int. J. Cont. Math. Sci. 7 (2012), 363–368.
  • M. Bahsi, S. Solak, On the matrices with Harmonic numbers, Gazi University J.Science 23 (4),(2010), 445-448.
  • J. Zhou, X. Chen, Z. Jiang, The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers, Math. Probl. Eng.Article ID 672398, 5 (2014).
  • R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
  • R.Graham, D. Knuth, K. Patashnik, Concrete Mathematics, Addison Wesley, 1989.
  • R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.
There are 9 citations in total.

Details

Primary Language English
Authors

Naim Tuglu

Can Kızılateş

Publication Date May 28, 2015
Published in Issue Year 2015 Volume: 28 Issue: 3

Cite

APA Tuglu, N., & Kızılateş, C. (2015). On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers. Gazi University Journal of Science, 28(3), 497-501. https://izlik.org/JA79MS93NN
AMA 1.Tuglu N, Kızılateş C. On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers. Gazi University Journal of Science. 2015;28(3):497-501. https://izlik.org/JA79MS93NN
Chicago Tuglu, Naim, and Can Kızılateş. 2015. “On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers”. Gazi University Journal of Science 28 (3): 497-501. https://izlik.org/JA79MS93NN.
EndNote Tuglu N, Kızılateş C (October 1, 2015) On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers. Gazi University Journal of Science 28 3 497–501.
IEEE [1]N. Tuglu and C. Kızılateş, “On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers”, Gazi University Journal of Science, vol. 28, no. 3, pp. 497–501, Oct. 2015, [Online]. Available: https://izlik.org/JA79MS93NN
ISNAD Tuglu, Naim - Kızılateş, Can. “On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers”. Gazi University Journal of Science 28/3 (October 1, 2015): 497-501. https://izlik.org/JA79MS93NN.
JAMA 1.Tuglu N, Kızılateş C. On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers. Gazi University Journal of Science. 2015;28:497–501.
MLA Tuglu, Naim, and Can Kızılateş. “On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers”. Gazi University Journal of Science, vol. 28, no. 3, Oct. 2015, pp. 497-01, https://izlik.org/JA79MS93NN.
Vancouver 1.Tuglu N, Kızılateş C. On the Norms of Some Special MatricesWith the Harmonic Fibonacci Numbers. Gazi University Journal of Science [Internet]. 2015 Oct. 1;28(3):497-501. Available from: https://izlik.org/JA79MS93NN