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

Abstract

Abstract Let us define A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ to be a n × n $n \times n$ r-circulant matrix. The entries in the first row of A = C r ( a 0 , a 1 , … , a n − 1 ) $A=C_{r}(a_{0},a_{1},\ldots,a_{n-1})$ are a i = P i $a_{i}=P_{i}$ , a i = Q i $a_{i}=Q_{i}$ , a i = P i 2 $a_{i}=P_{i}^{2}$ or a i = Q i 2 $a_{i}=Q_{i}^{2}$ ( i = 0 , 1 , 2 , … , n − 1 $i=0, 1, 2, \ldots, n-1$ ), where P i $P_{i}$ and Q i $Q_{i}$ 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.

Keywords

• Pell numbers
• Pell-Lucas numbers
• r-circulant matrix
• spectral norm