IJPAM: Volume 112, No. 1 (2017)
MATRICES WITH THE JACOBSTHAL AND JACOBSTHAL
LUCAS NUMBERS , S. Yaşamalı
Department of Mathematics
Science and Art Faculty
Campus, 27310, Gaziantep, TURKEY
and After that we obtain some bounds related to the spectral norms of Hadamard and Kronecker product of these matrices.
Received: June 25, 2016
Revised: January 11, 2017
Published: January 26, 2017
AMS Subject Classification: 15A36, 15A45, 15A60
Key Words and Phrases: Jacobsthal number, Jacobsthal Lucas number, circulant matrix, norm
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.
- A. F. Horadam, Jacobsthal representation numbers, The Fibonacci Quarterly, 34, No. 1 (1996), 40-54.
- T. Koshy, Fibanacci and Lucas Numbers with Applications, John Wiley and Sons Inc., NY, 2001.
- N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences, 2006.
- G. Zielke, Some remarks on matrix norms, condition numbers and error estimates for linear equations, Linear Algebra and its Applications, 110 (1988), 29-41.
- R. Mathias, The spectral norm of nonnegative matrix, Linear Algebra and its Applications, 131 (1990), 269-284.
- R. Reams, Hadamard inverses square roots and products of almost semidefinite matrices, Linear Algebra and its Applications, 288 (1999), 35-43.
- S. Solak, D. Bozkurt, On the spectral norms of Cauchy-Toeplitz and Cauchy-Henkel matrices, Appl. Math. Comput., 140 (2003), 231-238.
- S. Solak, On the norms of circulant matrices with the Fibonocci and Lucas numbers, Applied Mathematics and Computation, 160 (2005), 125-132.
- S. Shen, J. Cen, On the bounds for the norms of r-circulant matrices with the Fibonocci and Lucas numbers, Appl. Math. Comput., 216 (2010), 2891-2897.
- S. Shen, On the spectral norms of r-circulant matrices with the k-Fibonocci and k-Lucas numbers, Int. J. Contemp. Math. Sciences, 5, No. 12 (2010), 569-578.
- R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
- Ş. Uygun, The -Jacobsthal and -Jacobsthal Lucas sequences, Applied Mathematical Sciences, 70, No. 9 (2015), 3467-3476.
- K. Uslu, N. Taşkara, Ş. Uygun, The relations among Fibonacci, Lucas and generalized Fibonacci numbers and the spectral norms of the matrices of involving these numbers, Ars Combinatoria, 102 (2011), 183-192.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 93 - 102