SIAM Journal on Matrix Analysis and Applications
Structured Pseudospectra for Small Perturbations
SIAM Journal on Matrix Analysis and Applications
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The &egr;-pseudospectrum of a matrix $A$ is the subset of the complex plane consisting of all eigenvalues of complex matrices within a distance &egr; of $A$, measured by the operator 2-norm. Given a nonderogatory matrix $A_0$, for small $\epsilon 0, we show that the &egr;-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.