Minimal sets alternative to minimal Geršgorin sets

The concept of minimal Geršgorin set was introduced by Richard Varga (1965) in [10], and investigated in details in his book Geršgorin 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 Geršgorin theorem, was introduced by Juan Manuel Peña (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.