Research Article

ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS

Volume: 37 Number: 2 February 1, 2008
  • M. Akbulak
  • D. Bozkurt
EN TR

ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS

Abstract

Let us define A = [aij ] and B = [bij ] as n × n Toeplitz matrices such that aij ≡ Fi−j and bij ≡ Li−j where F and L denote the usual Fibonacci and Lucas numbers, respectively. We have found upper and lower bounds for the spectral norms of these matrices

Keywords

References

  1. Karaduman, E. An application of Fibonacci numbers in matrices, Applied Mathematics and Computation 147, 903–908, 2004.
  2. Kayaba¸s, H. The applications of k-Fibonacci sequences (Sel¸cuk University Graduate School of Natural and Applied Science, Ms Thesis, 2006).
  3. Koshy, T. Fibonacci and Lucas Numbers with Applications (Wiley-Interscience Publications, 2001).
  4. Mathias, R. The spectral norm of nonnegative matrix, Linear Algebra and its Applications 131, 269–284, 1990.
  5. Reams, R. Hadamard inverses, square roots and products of almost semidefinite matrices, Linear Algebra and its Applications 288, 35–43, 1999.
  6. Solak, S. On the norms of circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation 160, 125–132, 2005.
  7. Vajda, S. Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications (Ellis Horwood Ltd., 1989).
  8. Zielke, G. Some remarks on matrix norms, condition numbers and error estimates for linear equations, Linear Algebra and its Applications 110, 29–41, 1988.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

M. Akbulak This is me

D. Bozkurt This is me

Publication Date

February 1, 2008

Submission Date

May 12, 2014

Acceptance Date

-

Published in Issue

Year 2008 Volume: 37 Number: 2

APA
Akbulak, M., & Bozkurt, D. (2008). ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics, 37(2), 89-95. https://izlik.org/JA67TK33ST
AMA
1.Akbulak M, Bozkurt D. ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics. 2008;37(2):89-95. https://izlik.org/JA67TK33ST
Chicago
Akbulak, M., and D. Bozkurt. 2008. “ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS”. Hacettepe Journal of Mathematics and Statistics 37 (2): 89-95. https://izlik.org/JA67TK33ST.
EndNote
Akbulak M, Bozkurt D (February 1, 2008) ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics 37 2 89–95.
IEEE
[1]M. Akbulak and D. Bozkurt, “ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS”, Hacettepe Journal of Mathematics and Statistics, vol. 37, no. 2, pp. 89–95, Feb. 2008, [Online]. Available: https://izlik.org/JA67TK33ST
ISNAD
Akbulak, M. - Bozkurt, D. “ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS”. Hacettepe Journal of Mathematics and Statistics 37/2 (February 1, 2008): 89-95. https://izlik.org/JA67TK33ST.
JAMA
1.Akbulak M, Bozkurt D. ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics. 2008;37:89–95.
MLA
Akbulak, M., and D. Bozkurt. “ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS”. Hacettepe Journal of Mathematics and Statistics, vol. 37, no. 2, Feb. 2008, pp. 89-95, https://izlik.org/JA67TK33ST.
Vancouver
1.M. Akbulak, D. Bozkurt. ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics [Internet]. 2008 Feb. 1;37(2):89-95. Available from: https://izlik.org/JA67TK33ST