Structured Pseudospectra for Small Perturbations

In this paper we study the shape and growth of structured pseudospectra for small matrix perturbations of the form $A \leadsto A_\Delta=A+B\Delta C$, $\Delta \in \boldsymbol{\Delta}$, $\|\Delta\|\leq \delta$. It is shown that the properly scaled pseudospectra components converge to nontrivial limit sets as $\delta$ tends to 0. We discuss the relationship of these limit sets with $\mu$-values and structured eigenvalue condition numbers for multiple eigenvalues.

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