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Functional Analysis

Multiplicities of the structured pseudoeigenvalues

Profile image of Juan-Miguel Gracia MeleroJuan-Miguel Gracia Melero

2009

Abstract

The structured pseudospectra of a matrix A are sets of complex numbers that are eigenvalues of matrices X which are near to A and have the same entries as A at a fixed set of places. The sum of multiplicities of the eigenvalues of X inside each connected component of the structured pseudospectra of A does not depend on X. This fact is known, but not so much as it should be. For this reason, we give here an elementary and detailed proof of the result.

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