DMS Linear Algebra/Algebra Seminar

Title: On Pseudospectra and Norm Behavior of Matrices

Abstract: Eigenvalues are a useful tool for studying normal matrices.

Their eigenvectors can be taken to be orthogonal, and then they can be unitarily diagonalized. In contrast, non-normal matrices lack an orthogonal basis of eigenvectors. Thus, additional tools such as the numerical range and the pseudospectra are interesting for analyzing them.

This talk will introduce the theory of pseudospectra and discuss the norm behavior of matrices that have identical and super-identical pseudospectra.