  We propose a general framework to study the stability of the subspace spanned
by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when
a small perturbation is added. This problem is relevant in various contexts,
including quantum dissipation (${\bf H}_0$ is then the Hamiltonian) and risk
control (in which case ${\bf H}_0$ is the assets return correlation matrix). We
specialize our results for the case of a Gaussian Orthogonal ${\bf H}_0$, or
when ${\bf H}_0$ is a correlation matrix. We illustrate the usefulness of our
framework using financial data.
