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

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• 作者：Ralph John de la Cruz ; ^{rjdelacruz@math.upd.edu.ph} ; Kennett dela Rosa ^{prkdelarosa@math.upd.edu.ph}
• 关键词：11E39 ; 15A21 ; 15A23 ; 15B10
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：517
• 期：Complete
• 页码：53-62
• 全文大小：300 K
• 卷排序：517

文摘

A 2n×2n2n×2n complex matrix A   is symplectic if A⊤[0I−I0]A=[0I−I0]. If A   is symplectic and rank(A−I)=1rank(A−I)=1, then it is called a J-symmetry. For each n  , we prove that every 2n×2n2n×2n symplectic matrix M   is a product of n+1n+1 commutators of J-symmetries and this number cannot be smaller for some M.