Hamiltonian square roots of skew-Hamiltonian matrices revisited Original Research Article

Recently, H. Fassbender et al. [Linear Algebra Appl. 287 (1999) 125] proved the following theorem: Every real skew-Hamiltonian matrix W has a real Hamiltonian square root H, i.e., H2=W. We prove an analog of this theorem for complex matrices. Our approach may be of independent interest, namely, we use the polar decomposition of a nonsingular operator acting in a space with the symplectic inner product.