Question: (i) Explain why the eigenvalues of A must lie in its refined Gerschgorin domain D*A = DAT DA. (ii) Find the refined Gerschgorin domains for

(i) Explain why the eigenvalues of A must lie in its refined Gerschgorin domain D*A = DAT DA.
(ii) Find the refined Gerschgorin domains for each of the matrices in Exercise 10.3.22 and confirm the result in part (i).

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