摘要
OIn-InO是单位辛矩阵,若A∈C2n×2n满足AH=A,(JA)H=JA,则称A为Hermitian Hamilton矩阵,所有2n×2n阶Hermitian Hamilton矩阵的全体记为HHC2n×2n。本文考虑问题P:给定X∈C2n×p,Λ=diag(λ1,λ2,…,λp)∈Cp×p,求A,B∈HHC2n×2n使得AX=BXΛ。文中首先讨论了HHC2n×2n中元素的结构,然后给出了问题P的解的表达式。
Let J=OI_n-I_nO be a unit symplectic matrix,A∈C^(2n×2n) is called to be a Hermitian-Hamilton matrix if A^H=A and (JA)~H=JA,the set of all 2n×2n Hermitian-Hamilton matrices is denoted by HHC^(2n×2n).This paper discusses the following problem:Problem P.Given X∈C^(2n×p),Λ=diag(λ_1,λ_2,…,λ_p)∈C^(p×p),find A,B∈HHC^(2n×2n) such that AX=BXΛ。In this note,the structure of matrices in the set of HHC^(2n×2n) is analyzed,and the explicit representation of Problem P is given.
出处
《华东船舶工业学院学报》
2004年第6期25-28,共4页
Journal of East China Shipbuilding Institute(Natural Science Edition)
基金
国家自然科学基金资助项目(编号10271055)
