The Eigenvalues Problem for Complex Hamilton Matrix

In this paper, we focus on the conditions under which the eigenvalues of complex Hamiltonian matrices are symmetric with respect to the real and imaginary axis, and the sufficient conditions that the eigenvalues of complex Hamiltonian matrices are the real or the pure imaginary number are obtained. In the end, a class of complex Hamiltonian matrices whose eigenvalues are symme- tric with respect to the real and the imaginary axis are obtained.