Hi, I have a matrix of an ODE which yields complex eigenvalues and eigenvectors. It is therefore not Hermitian. How can I further analyse the properties of the matrix in a Hilbert space? The idea is to reveal the properties of stability and instability of the matrix. D_2 and D_1 are the second and first order derivatives respectively, and a and b are real numbers. I thought of treating the two operators as x² and x and solve the quadratic equation, however, this does not really give much more information.