Exclusion and Inclusion Intervals for the Real Eigenvalues of Positive Matrices
Juan Manuel Peña · SIAM Journal on Matrix Analysis and Applications · 2005
Given a real matrix, we analyze an openinterval, called a row exclusion interval, such that the real eigenvalues do not belong to it. We characterize when the row exclusion interval is nonempty. In addition to the exclusion interval, inclusion intervals for the real eigenvalues, alternative to those provided by the Gerschgorin disks, are also considered for matrices whose off-diagonal entries present a restricted dispersion. The results are applied to obtain a sharp upper bound for the real eigenvalues different from 1 of a positive stochastic matrix and a sufficient condition for the stability of a negative matrix, among other applications.