Hon Leung Lee; Minimizing Distance to an Orthogonally Invariant Matrix Set

January 27, 2015, 4:00pm
GUG 204
Hon Leung Lee, Depart­ments of Mathematics, UW.
Minimizing Distance to an Orthogonally Invariant Matrix Set

Abstract: The problem of finding the closest point in a set, with respect to Euclidean distance, arises frequently in applications. In this talk we focus on orthogonally invariant matrix sets and provide a framework for computing and counting the real smooth critical points of this minimization problem, as well as finding the minimizers. The key results are the “transfer principles” that allow calculations to be done in the Euclidean space containing the vectors of singular values of the members in the matrix set. Running examples include Eckart-Young theorem and finding the nearest essential matrix. This is a joint work with Dmitriy Drusvyatskiy and Rekha Thomas.