Take any diagonal matrix. Then the eigenvalues are the diagonal entries but the the Gerschgorin discs are points centred at the diagonal entries. So we can't remove one of the discs from the set.
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CSI of Charles University
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Take any diagonal matrix. Then the eigenvalues are the diagonal entries but the the Gerschgorin discs are points centred at the diagonal entries. So we can't remove one of the discs from the set.