Eigenvector dynamics: theory and some applications

Details Eigenvector dynamics: theory and some applications Eigenvector dynamics: theory and some applications

2011-08-22

arxiv.org/abs/1108.4258v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

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.

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