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

摘要

Let J is an element of R-nxn be a normal matrix such that J(2) = -I-n. A matrix M is an element of C-nxn 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/skewHamiltonian 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. (C) 2019 Elsevier Inc. All rights reserved.