  We present a Gershgorin's type result on the localisation of the spectrum of
a matrix. Our method is elementary and relies upon the method of Schur
complements, furthermore it outperforms the one based on the Cassini ovals of
Ostrovski and Brauer. Furthermore, it yields estimates that hold without major
differences in the cases of both scalar and operator matrices. Several
refinements of known results are obtained.
