Estimates of eigenspaces and eigenvalues of a matrix

Łukasz Struski, Jacek Tabor, Piotr Zgliczyński

Published 2014-10-21Version 1

We discuss techniques for rigorous estimations of eigenspaces and eigenvalues of a matrix. We give two kinds of results. In the first one, which is a generalization of Gerschgorin theorems, we consider blocks on the diagonal and provide bounds for eigenvectors. Second one is based on ideas from the dynamics of hyperbolic dynamical systems. We introduce the notion of dominated matrix and for such matrices we present a theorem which allow us to rigorously estimate eigenspaces and eigenvalues. In particular, we can deal with clusters of eigenvalues and their eigenspaces.