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.
Highlights
Special matrices is a widely studied subject in matrix analysis
Lots of article have been written so far, which concern estimates for spectral norms of circulant and r-circulant matrices, which have connections with signal and image processing, time series analysis and many other problems
We thicken the identities of estimations for spectral norms of r-circulant matrices with the Pell and Pell-Lucas numbers
Summary
Special matrices is a widely studied subject in matrix analysis. Special matrices whose entries are well-known number sequences have become a very interesting research subject in recent years and many authors have obtained some good results in this area. We derive expressions of spectral norms for r-circulant matrices. We thicken the identities of estimations for spectral norms of r-circulant matrices with the Pell and Pell-Lucas numbers. If we start from n = , the Pell and Pell-Lucas sequence are given by n:. The following sum formulas for the Pell and Pell-Lucas numbers are well known [ , ]: n. Let r = , the matrix C is called a circulant matrix [ ]
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