Birkhoff's polytope and unistochastic matrices, N=3 and N=4

Details Birkhoff's polytope and unistochastic matrices, N=3 and N=4 Birkhoff's polytope and unistochastic matrices, N=3 and N=4

2004-02-19

arxiv.org/abs/math/0402325v2

Final version in Commun. Math. Phys. 259, 307-324 (2005)

Mathematics

Combinatorics

30 pages, 4 figures

Scientific paper

10.1007/s00220-005-1392-8

The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic matrices as a subset of Birkhoff's polytope. For N=3 we present fairly complete results. For N=4 partial results are obtained. An interesting difference between the two cases is that there is a ball of unistochastic matrices around the van der Waerden matrix for N=3, while this is not the case for N=4.

Affiliated with

Also associated with

No associations

Rating

Birkhoff's polytope and unistochastic matrices, N=3 and N=4 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Birkhoff's polytope and unistochastic matrices, N=3 and N=4, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Birkhoff's polytope and unistochastic matrices, N=3 and N=4 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-709276