Eigenvector dynamics: theory and some applications
We propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0, when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and risk control (in which case H0 is the assets return correlation matrix). We specialise our results for the case of a Gaussian Orthogonal H0, or when H0 is a correlation matrix. We illustrate the usefulness of our framework using financial data.