Vol. 9, No. 3, 2016

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Explicit bounds for the pseudospectra of various classes of matrices and operators

Feixue Gong, Olivia Meyerson, Jeremy Meza, Mihai Stoiciu and Abigail Ward

Vol. 9 (2016), No. 3, 517–540
Abstract

We study the $\epsilon$-pseudospectra ${\sigma }_{\epsilon }\left(A\right)$ of square matrices $A\in {ℂ}^{N×N}$. We give a complete characterization of the $\epsilon$-pseudospectra of $2×2$ matrices and describe the asymptotic behavior (as $\epsilon \to 0$) of ${\sigma }_{\epsilon }\left(A\right)$ for every square matrix $A$. We also present explicit upper and lower bounds for the $\epsilon$-pseudospectra of bidiagonal matrices, as well as for finite-rank operators.

Keywords
spectrum, pseudospectrum, bidiagonal matrices, perturbation of eigenvalues
Mathematical Subject Classification 2010
Primary: 15A18, 15A60, 47A10, 65F15