Hamiltonian and Linear-Space Structure for Damped Oscillators: I.   General Theory
  The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis. 
S.C. Chee, Alec Maassen van den Brink, and K. Young