On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers

Abstract

Let us define $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ to be a $n \times n$ r-circulant matrix. The entries in the first row of $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ are $a_{i}=P_{i}$ , $a_{i}=Q_{i}$ , $a_{i}=P_{i}^{2}$ or $a_{i}=Q_{i}^{2}$ ( $i=0, 1, 2, \ldots, n-1$ ), where $P_{i}$ and $Q_{i}$ are the ith Pell and Pell-Lucas numbers, respectively. We find some bounds estimation of the spectral norm for r-Circulant matrices with Pell and Pell-Lucas numbers.