A note on equivalent conditions for majorization

Roberto Bruno; Ugo Vaccaro; Roberto Bruno; Ugo Vaccaro

doi:10.3934/math.2024419

AIMS Mathematics

2024, Volume 9, Issue 4: 8641-8660. doi: 10.3934/math.2024419

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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

Received: 04 December 2023 Revised: 19 February 2024 Accepted: 20 February 2024 Published: 29 February 2024
MSC : 94A17, 15A45, 39B62, 47A63

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.
- majorization,
- entropy,
- row-stochastic matrices,
- column-stochastic matrices,
- Schur-concave functions
Citation: Roberto Bruno, Ugo Vaccaro. A note on equivalent conditions for majorization[J]. AIMS Mathematics, 2024, 9(4): 8641-8660. doi: 10.3934/math.2024419

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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.

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