Expected Pseudospectral Area of Random Compressions

The spectrum of a matrix compression Q*AQ can be much more sensitive to small perturbations than the original matrix A, posing a challenge to the analysis of Rayleigh-Ritz methods. This talk considers the pseudospectrum of Q*AQ for Haar randomly sampled Q, i.e. the set of eigenvalues of all perturbations to Q*AQ. We describe some mild conditions under which its expected area is small.