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The p-norm of circulant matrices via Fourier analysis

Sahasranand, KR (2021) The p-norm of circulant matrices via Fourier analysis. In: Concrete Operators, 9 (1). pp. 1-5.

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Official URL: https://doi.org/10.1515/conop-2021-0123


A recent work derived expressions for the induced p-norm of a special class of circulant matrices A(n, a, b) ϵ �n�n, with the diagonal entries equal to a ϵ � and the off-diagonal entries equal to b � 0. We provide shorter proofs for all the results therein using Fourier analysis. The key observation is that a circulant matrix is diagonalized by a DFT matrix. The results comprise an exact expression for |A|p, 1 � p � �, where A = A(n, a, b), a � 0 and for |A|2 where A = A(n, -a, b), a � 0; for the other p-norms of A(n, -a, b), 2 < p < �, upper and lower bounds are derived. © 2022 K. R. Sahasranand, published by De Gruyter.

Item Type: Journal Article
Publication: Concrete Operators
Publisher: De Gruyter Open Ltd
Additional Information: The copyright for this article belongs to Authors
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 21 Feb 2022 12:06
Last Modified: 21 Feb 2022 12:06
URI: http://eprints.iisc.ac.in/id/eprint/71416

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