On rigorous estimates of eigenspaces and eigenvalues of a matrix

Abstract

We present a method of cones for rigorous estimations of eigenvectors, eigenspaces and eigenvalues of a matrix. The key notion is the cone-domination and is inspired by ideas from hyperbolic dynamical systems. We present theorems which allow to rigorously locate the spectrum of the matrix and the eigenspaces, also multidimensional ones in case of eigenvalues of multiplicity greater than one or clusters of close eigenvalues. In case of isolated eigenvalue we show that the our method give the same or better estimates than ones known in literature.