Generalized Inverse Eigenvalue Problem of a Class of Hermitian-Hamilton Matrices
Yongxin Yuan, Hua Dai · 2004
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.