2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58726We 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 modelSpectral TheoryMathematical Physics65F15; 65F22; 15A18; 15A52; 47A75; 47B80; 60H25text