Journal of Linear Algebra
Eigenvalue continuity, Gerˇsgorin disk theorem, Root continuity
Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.
Li, Chi-Kwong and Zhang, Fuzhen, "Eigenvalue continuity and Gersgorin's theorem" (2019). Mathematics Faculty Articles. 304.