The Birkhoff theorem for unitary matrices of arbitrary dimensions

Stijn De Baerdemacker; Alexis De Vos; Lin Chen; Li Yu

doi:10.1016/j.laa.2016.10.028

The Birkhoff theorem for unitary matrices of arbitrary dimensions

Stijn De Baerdemacker^*
, Alexis De Vos
, Lin Chen
, Li Yu

^*Corresponding author for this work

School of Mathematical Sciences

Ghent University
National Institute of Informatics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	151-164
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	514
DOIs	https://doi.org/10.1016/j.laa.2016.10.028
State	Published - 1 Feb 2017

Keywords

Birkhoff's theorem
Doubly stochastic matrix
Irreducible representation
Unitary matrix

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10.1016/j.laa.2016.10.028

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title = "The Birkhoff theorem for unitary matrices of arbitrary dimensions",

abstract = "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.",

keywords = "Birkhoff's theorem, Doubly stochastic matrix, Irreducible representation, Unitary matrix",

author = "\{De Baerdemacker\}, Stijn and \{De Vos\}, Alexis and Lin Chen and Li Yu",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2017",

month = feb,

day = "1",

doi = "10.1016/j.laa.2016.10.028",

language = "英语",

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T1 - The Birkhoff theorem for unitary matrices of arbitrary dimensions

AU - De Baerdemacker, Stijn

AU - De Vos, Alexis

AU - Chen, Lin

AU - Yu, Li

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Birkhoff's theorem

KW - Doubly stochastic matrix

KW - Irreducible representation

KW - Unitary matrix

UR - https://www.scopus.com/pages/publications/84995662362

U2 - 10.1016/j.laa.2016.10.028

DO - 10.1016/j.laa.2016.10.028

M3 - 文章

AN - SCOPUS:84995662362

SN - 0024-3795

VL - 514

SP - 151

EP - 164

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

The Birkhoff theorem for unitary matrices of arbitrary dimensions

Abstract

Keywords

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