Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416191 | Linear Algebra and its Applications | 2016 | 14 Pages |
Abstract
The Birkhoff's theorem states that any doubly stochastic matrix lies inside a convex polytope with the permutation matrices at the corners. We prove that any unitary matrix with equal line sums can also be written as a sum of permutation matrices (with sum of weights equal 1). Furthermore, when the matrix dimension is prime, we prove that the unitary matrix lies inside a convex complex Birkhoff polytope.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alexis De Vos, Stijn De Baerdemacker,