 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2007/p/4/b/solution

The second part of the Gershgorin circle theorem states that if a union of

k

of the discs is disjoint from every remaining disc, that union contains exactly

k

eigenvalues, counted with algebraic multiplicity. In particular, a single isolated disc contains precisely one eigenvalue. Connected components of the full union therefore carry the corresponding disc counts.

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