Pitfalls of using Geršgorin Theorem in Opinion Dynamics

Finding a range that contains all the eigenvalues of a certain matrix is extremely important for giving insight into the behaviour of evolving systems governed by linear equations. One such range, which is particularly well-known, is the Gersgorin set. Although Gersgorm theorem is very simple and elegant, it hides a trap for misinterpretation, which has already happened in different application areas. The aim of this paper is to inform potential users of the Gersgorin theorem about common pitfalls of its inadequate interpretation, explain one such situation where a misinterpretation produced results which are not correct in general, in order to provide an alternative (but correct) analysis and open a path for a future extension of this interesting topic.