Each 2n-by-2n complex symplectic matrix is a product of n+1 commutators of J-symmetries

Each 2n-by-2n complex symplectic matrix is a product of n+1 commutators of J-symmetries

A 2n×2n complex matrix A is symplectic if A⊤[0I−I0]A=[0I−I0]. If A is symplectic and rank(A−I)=1, then it is called a J-symmetry. For each n, we prove that every 2n×2n symplectic matrix M is a product of n+1 commutators of J-symmetries and this number cannot be smaller for some M.

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Bibliographische Detailangaben
Veröffentlicht in:Linear algebra and its applications 2017-03, Vol.517, p.53-62
Hauptverfasser: de la Cruz, Ralph John, dela Rosa, Kennett
Format: Artikel
Sprache:eng
Schlagworte:
Commutators
Complex systems
Graph theory
J-symmetry
Linear algebra
Mathematical analysis
Matrix
Matrix factorization
Matrix methods
Symmetry
Symplectic
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Zusammenfassung:A 2n×2n complex matrix A is symplectic if A⊤[0I−I0]A=[0I−I0]. If A is symplectic and rank(A−I)=1, then it is called a J-symmetry. For each n, we prove that every 2n×2n symplectic matrix M is a product of n+1 commutators of J-symmetries and this number cannot be smaller for some M.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2016.12.006