TITLE:
On the Norms of r-Hankel Matrices Involving Fibonacci and Lucas Numbers
AUTHORS:
Hasan Gökbaş, Hasan Köse
KEYWORDS:
Euclidean Norm, Spectral Norm, r-Hankel Matrix, Fibonacci Numbers, Lucas Numbers
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.7,
July
10,
2018
ABSTRACT: Let us define A=Hr=(aij)to be n×nr-Hankel
matrix. The entries of matrix A are Fn=Fi+j-2or Ln=Fi+j-2where Fnand Lndenote the usual Fibonacci and Lucas numbers,
respectively. Then, we
obtained upper and lower bounds for the spectral norm of matrix A. We compared our bounds with exact
value of matrix A’s spectral norm.
These kinds of matrices have connections with
signal and image processing, time series analysis and many other problems.