Diagonalization of continuous families of matrices over an interval

Abstract

We start by reviewing the general case of diagonalizing a single matrix. A necessary and sufficient condition is that the algebraic multiplicity coincides with the geometric multiplicity for each eignenvalue. We then consider the case where the case were we have a continuous family of matrices over an interval. In this presentation, we will study when such a family can be diagonalized. The primary reference of this topic is a result from Grove and Pedersen.

Faculty Mentor: Dr. Cristian Ivanescu