Bouthat, Ludovick ; Khare, Apoorva ; Mashreghi, Javad ; Morneau-Guérin, Frédéric (2021) The p-norm of circulant matrices Linear and Multilinear Algebra . pp. 1-13. ISSN 0308-1087
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Official URL: http://doi.org/10.1080/03081087.2021.1983513
Related URL: http://dx.doi.org/10.1080/03081087.2021.1983513
Abstract
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 non negative 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.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Taylor and Francis Ltd. |
| Keywords: | Circulant matrices; p-norms; Doubly stochastic matrices |
| ID Code: | 127309 |
| Deposited On: | 17 Oct 2022 05:12 |
| Last Modified: | 17 Oct 2022 05:12 |
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