Eigenvalue bounds for matrices.

Abstract

Eigenvalues are characteristic of linear operators. Once the spectrum of a matrix is known then its Jordan Canonical form can be determined which simplifies the un- derstanding of the matrix. For large matrices and spectral analysis sometimes it is only necessary to know the eigenvalues of smallest and largest absolute values. Hence we consider various strategies of bounding the spectrum in the complex plane. Such bounds may be numerically improved by various algorithms. The minimal and maximal eigenvalues are crucial to determine the condition number of linear systems.