On the Norms of Toeplitz and Hankel Matrices with Pell Numbers

摘要

Let us define A = [a_(ij)]_(i,j)~(n-1)=0 and B = [b_(ij)]_(i,j)~(n-1))=0 as n x n Toeplitz and Hankel matrices, respectively, such that a_(ij) = P_(i-j) and b_(ij) = P_(i+j), where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.