SCHUR'S INEQUALITY FOR EIGENVALUES OF MATRICES
Abstract
In this thesis, we study Schur's inequality, which is a consequence of the Schur decomposition theorem. We give applications and generalizations of this inequality. In addition, we discuss several refinements of this inequality related to measures of non-normality of matrices. Moreover, we present bounds for the zero of polynomials and several estimates concerning the localization of eigenvalues of complex matrices, which are based on Schur's inequality.