Title: From spectra to pseudospectra: An overview of normal to nonnormal matrices

Abstract: Eigenvalues have had a great of success in a wide range of fields both within mathematics and in the sciences. Yet, ask any numerical analyst for example and they will tell you eigenvalues don’t always give you the full picture of a problem. Indeed, we oftentimes see normal matrices and operators, that the behavior of their eigenvalues and functions motivates most of our intuition about most square matrices. We briefly discuss alternative quantities such as the condition number of a matrix; we then finalize by talking about Pseudospectra, some results and its applications. The talk is intended to be accessible to both theoretical and applied mathematicians as well as anyone that actively uses linear algebra in applications.