Year 2017, Volume 4 , Issue 1, Pages 13 - 21 2017-01-11

On the norms of r-circulant matrices with generalized Fibonacci numbers

Amara CHANDOUL [1]


In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices.
Matrix norm, r-circulant matrices, Generalized Fibonacci numbers
  • [1] D. Bozkurt, T. Y. Tam, Determinants and inverses of r􀀀circulant matrices associated with a number sequences, Linear and Multilinear Algebra 63(10) (2015) 2079–2088.
  • [2] H. Civciv, R. Turkmen, Notes on norms of circulant matrices with Lucas numbers, Int. J. Inf. Syst. Sci. 4(1) (2008) 142–147.
  • [3] C. He, J. Ma, K. Zhang, Z. Wang, The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl. Article ID 72 (2015) 1–10.
  • [4] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • [5] R. Mathias, The spectral norm of nonnegative matrix, Linear Algebra Appl. 139 (1990), 269–284.
  • [6] A. Nalli, M. Sen, On the norms of circulant matrices with generalized Fibonacci numbers, Selçuk J. Appl. Math. 11(1) (2010) 107–116.
  • [7] T. Koshy, Fibonacci and Lucas Numbers with Application, John Wiley and Sons, Inc., 2001.
  • [8] S. Shen, J. Cen, On the norms of r􀀀circulant matrices with Fibonacci and Lucas numbers, Appl.
  • [9] S. Solak, On the norms of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 160(1) (2005) 125–132.
  • [10] S. Solak, Erratum to "On the norms of circulant matrices with Fibonacci and Lucas numbers" [Appl. Math. Comput. 160(1) (2005) 125-132], Appl. Math. Comput. 190(2) (2007) 1855–1856.
  • [11] N. Tuglu, C. Kizilates, On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl. Article ID 253 (2015) 1–11.
  • [12] S. Vajda, Fibonacci and Lucas numbers and Golden Section, John Wiley and Sons, Inc., 1989.
Subjects Engineering
Journal Section Articles
Authors

Author: Amara CHANDOUL

Dates

Publication Date : January 11, 2017

Bibtex @research article { jacodesmath284552, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2017}, volume = {4}, pages = {13 - 21}, doi = {10.13069/jacodesmath.12813}, title = {On the norms of r-circulant matrices with generalized Fibonacci numbers}, key = {cite}, author = {Chandoul, Amara} }
APA Chandoul, A . (2017). On the norms of r-circulant matrices with generalized Fibonacci numbers . Journal of Algebra Combinatorics Discrete Structures and Applications , 4 (1) , 13-21 . DOI: 10.13069/jacodesmath.12813
MLA Chandoul, A . "On the norms of r-circulant matrices with generalized Fibonacci numbers" . Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 13-21 <https://dergipark.org.tr/en/pub/jacodesmath/issue/27044/284552>
Chicago Chandoul, A . "On the norms of r-circulant matrices with generalized Fibonacci numbers". Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2017 ): 13-21
RIS TY - JOUR T1 - On the norms of r-circulant matrices with generalized Fibonacci numbers AU - Amara Chandoul Y1 - 2017 PY - 2017 N1 - doi: 10.13069/jacodesmath.12813 DO - 10.13069/jacodesmath.12813 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 13 EP - 21 VL - 4 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.12813 UR - https://doi.org/10.13069/jacodesmath.12813 Y2 - 2020 ER -
EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications On the norms of r-circulant matrices with generalized Fibonacci numbers %A Amara Chandoul %T On the norms of r-circulant matrices with generalized Fibonacci numbers %D 2017 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 4 %N 1 %R doi: 10.13069/jacodesmath.12813 %U 10.13069/jacodesmath.12813
ISNAD Chandoul, Amara . "On the norms of r-circulant matrices with generalized Fibonacci numbers". Journal of Algebra Combinatorics Discrete Structures and Applications 4 / 1 (January 2017): 13-21 . https://doi.org/10.13069/jacodesmath.12813
AMA Chandoul A . On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 13-21.
Vancouver Chandoul A . On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017; 4(1): 13-21.