On the boundary of the pseudospectrum and its fault points

Abstract

The theme of this paper was motivated by the question: How effective are path-following procedures for tracing the pseudospectral boundary? The present study of the mathematical properties of the boundary of the pseudospectrum is the result. This boundary is generally made up piecewise smooth curves. We shown how the Schur triangular form of the matrix can be used to analyse dynamical properties of the singular points on these curves.