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The p-norm of circulant matrices

Bouthat, L and Khare, A and Mashreghi, J and Morneau-Guérin, F (2021) The p-norm of circulant matrices. In: Linear and Multilinear Algebra, 70 (21). pp. 7176-7188.

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Official URL: https://doi.org/10.1080/03081087.2021.1983513


In this note, we study the induced p-norm of circulant matrices A(n, ± a, b), acting as operators on the Euclidean space (Formula presented.). 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.

Item Type: Journal Article
Publication: Linear and Multilinear Algebra
Publisher: Taylor and Francis Ltd.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Circulant matrices; doubly stochastic matrices; p-norms
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 13 Jun 2023 05:45
Last Modified: 13 Jun 2023 05:45
URI: https://eprints.iisc.ac.in/id/eprint/81816

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