In this note, we study the induced p-norm of circulant matrices A(n,±a,b), acting as operators on the Euclidean space Rn. For circulant matrices whose entries are nonnegative real numbers, in particular for A(n,a,b), we provide an explicit formula for the p-norm, 1≤p≤∞. The calculation for A(n,−a,b) is more complex. The 2-norm is precisely determined. As for the other values of p, two different categories of upper and lower bounds are obtained. These bounds are optimal at the end points (i.e. p = 1 and p=∞) as well as at p = 2.
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Bouthat et al. (2021) studied this question.
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