Birkhoff ’ S Polytope and Unistochastic Matrices N = 3 and N = 4
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چکیده
The set of bistochastic or doubly stochastic N × 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.
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تاریخ انتشار 2004