A note on equivalent conditions for majorization

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

• majorization
• entropy
• row-stochastic matrices
• column-stochastic matrices
• schur-concave functions