On invariant subspaces of Hamiltonian matrices
Volker Mehrmann, Hongguo Xu · 2003
The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases: existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.