A Note on Structured Pseudospectra∗
نویسنده
چکیده
In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the unstructured pseudospectrum for matrix polynomials with Toeplitz, circulant, Hankel and symmetric structures. We conclude by giving a formula for structured pseudospectra of real matrix polynomials. The particular type of perturbations uses for this pseudospectra arises in control theory.
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