Spectral Properties of Random Non-self-adjoint Matrices and Operators
Abstract
Description
We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size. We also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace, but the eigenvalues do not determine the spectrum. Our results imply that the spectrum of the non-self-adjoint Anderson model changes suddenly as one passes to the infinite volume limit.
keywords: eigenvalues, spectral instability, matrices, computability, pseudospectrum, Schroedinger operator, Anderson model
keywords: eigenvalues, spectral instability, matrices, computability, pseudospectrum, Schroedinger operator, Anderson model