Abstract
An important tool in the study of majorization is a theorem due to Hardy, Littlewood, and Pólya (1929) which states that for x, yЄR n,x < y if and only if x = yP for some doubly stochastic matrix P.
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Marshall, A.W., Olkin, I., Arnold, B.C. (2010). Doubly Stochastic Matrices. In: Inequalities: Theory of Majorization and Its Applications. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68276-1_2
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DOI: https://doi.org/10.1007/978-0-387-68276-1_2
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