The Birkhoff theorem for unitary matrices of arbitrary dimensions

The Birkhoff theorem for unitary matrices of arbitrary dimensions

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimens...

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Veröffentlicht in:Linear algebra and its applications 2017-02, Vol.514, p.151-164
Hauptverfasser: De Baerdemacker, Stijn, De Vos, Alexis, Chen, Lin, Yu, Li
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Birkhoff's theorem
Doubly stochastic matrix
Irreducible representation
Linear algebra
Number theory
Polynomials
Sums
Theorems
Theory
Unitary matrix
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Zusammenfassung:It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for unitary matrices with equal line sums for arbitrary dimension.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.10.028