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Doubly Stochastic Matrices

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

An important tool in the study of majorization is a theorem due to Hardy, Littlewood, and Pólya (1929) which states that for x, yЄRn,x < y if and only if x = yP for some doubly stochastic matrix P.

Keywords

Convex Hull Extreme Point Permutation Matrix Convex Polytope Stochastic Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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