Abstract
In this note, we study the induced p-norm of circulant matrices , acting as operators on the Euclidean space . For circulant matrices whose entries are nonnegative real numbers, in particular for , we provide an explicit formula for the p-norm, . The calculation for 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 ) as well as at p = 2.
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