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Research Article | Open Access

A note on equivalent conditions for majorization

Roberto Bruno, Ugo Vaccaro( )
Department of Computer Science, University of Salerno, via Giovanni Paolo Ⅱ, 132, 84084 Fisciano (SA), Italy
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Abstract

In this paper, we introduced novel characterizations of the classical concept of majorization in terms of upper triangular (resp., lower triangular) row-stochastic matrices, and in terms of sequences of linear transforms on vectors. We use our new characterizations of majorization to derive an improved entropy inequality.

Keywords

majorizationentropyrow-stochastic matricescolumn-stochastic matricesSchur-concave functions
CLC number: 94A17, 15A45, 39B62, 47A63

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 8641-8660
DOI: 10.3934/math.2024419

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Bruno R, Vaccaro U. A note on equivalent conditions for majorization. AIMS Mathematics, 2024, 9(4): 8641-8660. https://doi.org/10.3934/math.2024419

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Received: 04 December 2023
Revised: 19 February 2024
Accepted: 20 February 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)