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Abstract: We study the concept matrix majorization: for two real matrices A and B having m rows we say that A majorizes B if there is a row-stochastic matrix X with AX = B. A special case is classical notion of vector majorization. Several properties and characterizations of matrix majorization are given. Moreover, interpretations of the concept in mathematical statistics are discussed and some combinatorial questions are studied. (Update)
Active bibliography (related documents): More All
0.6: Majorization, Polyhedra and Statistical Testing Problems. - Dahl (1997) (Correct)
0.2: Weak K-Majorization and Polyhedra - Dahl, Margot (1996) (Correct)
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BibTeX entry: (Update)
@article{ dahl99matrix,
author = "Geir Dahl",
title = "Matrix majorization",
journal = "Linear Algebra and its Applications",
volume = "288",
number = "1--3",
pages = "53--73",
year = "1999",
url = "citeseer.ist.psu.edu/dahl98matrix.html" }
Citations (may not include all citations):306 Inequalities: Theory of Majorization and Its Applications (context) - Marshall, Olkin - 1979
10 graphs and optimization (context) - Yemelichev, Kovalev et al. - 1984
8 Linear algebra and its Applications (context) - Ando, inequalities et al. - 1994
4 Pseudo experiments and majorization (context) - Dahl - 1984
2 The doubly stochastic matrices of a vector majorization (context) - Brualdi - 1984
1 The doubly stochastic matrices of a multivariate majorizatio.. (context) - Cheon, Lee - 1995
1 in and Y. Rinott. Comparison of measures, multivariate major.. (context) - Karl - 1983
1 Comments and complements to: Inequalities: Theory of Majoriz.. (context) - Bondar - 1994
1 volume 36 of Encyclopedia of Mathematics and its application.. (context) - Torgersen, Statistical - 1992
1 Reidel Publishing Comp (context) - Alberti, Uhlmann et al. - 1982
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