Stability of eigenvalues and spectral decompositions under linear perturbation (Q1870072)

Given a square matrix \(A\), a fixed perturbation matrix \(E\), and \(A+tE\) the linear perturbations depending on the complex parameter \(t\), the main results of the paper pertain to: a) classification of the eigenvalues of \(A\) with respect to \(E\) into infinitely stable, finitely stable and unstable eigenvalues, and correspondingly providing various characterizations; b) analysis of the effect of the linear perturbations \(A+tE\) on spectral decompositions of \(A\) by introducing the dissociation and geometric separation of eigenvalues of \(A\) with respect to \(E\) and by characterization of the sensitivity of spectral decompositions of \(A\); c) geometric framework for the family \(A+tE\) in order to analyze various sensitivity issues associated with eigenvalues and spectral decompositions of \(A\) graphically.