Extensions of Geršgorin Theory

In this proposal, I continue the work I have started together with Dr. Frank Hall in 2012 at Georgia State University, about Gergorin theory, its extensions and applications. In particular, we continue our study of the connection between the multiplicity of eigenvalues and their locations in the Gergorin region of matrices. Under the sight of this connection, we will try to come up with some sharper inclusion sets, for the eigenvalues of matrices belonging to known classes such as stochastic matrices.