On the concentration of spectral properties

We consider the problem of measuring the eigenvalues of a ran (cid: 173) domly drawn sample of points. We show that these values can be reliably estimated as can the sum of the tail of eigenvalues. Fur (cid: 173) thermore, the residuals when data is projected into a subspace is shown to be reliably estimated on a random sample. Experiments are presented that confirm the theoretical results.