Past exam of the options II course of the University of Oxford / 2007 / P / P4 / b

Gershgorin's second theorem states that a union of $k$ row discs separated from the union of all remaining discs contains exactly $k$ eigenvalues, counted with algebraic multiplicity. In particular a disc disjoint from every other disc contains exactly one eigenvalue. The same assertion holds for column discs by applying it to the transpose.