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Two types of eigenvalue continuity are commonly used in the literature.However, their meanings and the conditions under which continuities are usedare not always stated clearly. This can lead to some confusion and needs to beaddressed. In this note, we revisit the Ger\v{s}gorin disk theorem and clarifythe issue concerning the proofs of the theorem by continuity.

Eigenvalue continuity and Ger\v{s}gorin's theorem