Consider an n\times n deterministic matrix A and a random matrix M with independent standard Gaussian entries. In this talk I will discuss recent results that state that, if \|A\|\leq1 , for any \delta>0, with high probability A+\delta M has eigenvector condition number of order poly(n/\delta) and eigenvalue gaps of order poly(\delta/n), which implies that the randomly perturbed matrix has stable...