Effect of linear perturbation on spectra of matrices
The sensitivity of the eigenvalues of a matrix \(A\) under a linear perturbation \(A(t) = A + tE\) is studied. The aim of such studies is to learn about the split-up of repeated eigenvalues of \(A\) in \(A(t)\). It is known that there are essentially three kinds of behaviour here: In general there are finitely stable, infinitely stable, and unstable eigenvalues. This paper primarily studies perturbation effects on the unstable eigenvalues and looks at the distribution of the perturbed spectra. Isospectral perturbations \(E\) of \(A\) in \(A(t)\) for some or all values of \(t\) are also characterized here.
scientific article; zbMATH DE number 1956809