Generalized inverse eigenvalue problems for Hermitian and J-Hamiltonian/skew-Hamiltonian matrices

摘要

Let J ∈ Rn×n be a normal matrix such that J2=−In. A matrix M ∈ Cn×n is called J-Hamiltonian (J-skew-Hamiltonian) if (MJ)H=MJ((MJ)H=−MJ). In this paper, the generalized inverse eigenvalue problem for Hermitian and J-Hamiltonian/skew-Hamiltonian matrices is considered. The properties and structures of Hermitian and J-Hamiltonian/skew-Hamiltonian matrices are analyzed. The solvability conditions for the inverse problem are derived and the representation of the general solution is presented.