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.

Solution

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

 Solution (source code)