Acta Mathematica Vietnamica

, Volume 43, Issue 4, pp 675–700 | Cite as

Symmetric, Hankel-Symmetric, and Centrosymmetric Doubly Stochastic Matrices

  • Richard A. BrualdiEmail author
  • Lei Cao


We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel-symmetric, centrosymmetric, and both symmetric and Hankel-symmetric. We determine dimensions of these polytopes and classify their extreme points. We also determine a basis of the real vector spaces generated by permutation matrices with these special structures.


Matrix Permutation matrix Symmetric Hankel-symmetric Centrosymmetric Doubly stochastic Extreme point 

Mathematics Subject Classification (2010)

05C50 15B05 15B51 15B48 90C57 


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsGeorgian Court UniversityLakewoodUSA

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