Abstract
The e-pseudospectrum of a matrix $A$ is the subset of the complex plane consisting of all eigenvalues of complex matrices within a distance e of $A$, measured by the operator 2-norm. Given a nonderogatory matrix $A_0$, for small $\epsilon > 0, we show that the e-pseudospectrum of any matrix $A$ near $A_0$ consists of compact convex neighborhoods of the eigenvalues of $A_0$. Furthermore, the dependence of each of these neighborhoods on $A$ is Lipschitz.
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