Minimal sets alternative to minimal Gersgorin sets

The concept of minimal Gersgorin set was introduced by Richard Varga (1965) in [10], and investigated in details in his book Gersgorin and his circles (2004), [12]. On the other hand, another type of localization of real eigenvalues, which can be considered as an alternative to well-known Gersgorin theorem, was introduced by Juan Manuel Pena (2001) in [7]. Here we are combining these two approaches, in order to get two alternative tools for getting some information about real eigenvalues, or real part of eigenvalues. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.