On the spectral and Frobenius norm of a generalized Fibonacci r-circulant matrix

Abstract

<p>Consider the recursion g<sub>0</sub> = a, g<sub>1</sub> = b, g<sub>n</sub> = g<sub>n-1</sub> + g<sub>n-2</sub>, n = 2, 3, . . . . We compute the Frobenius norm of the r-circulant matrix corresponding to g<sub>0</sub>, . . . , g<sub>n-1</sub>. We also give three lower bounds (with equality conditions) for the spectral norm of this matrix. For this purpose, we present three ways to estimate the spectral norm from below in general.</p>