Eigenvalue resolution of self-adjoint matrices

Xuwen Zhu

Vol. 288 (2017), No. 1, 241–255

DOI: 10.2140/pjm.2017.288.241

Abstract

Resolution of a compact group action in the sense described by Albin and Melrose is applied to the conjugation action by the unitary group on self-adjoint matrices. It is shown that the eigenvalues are smooth on the resolved space and that the trivial bundle smoothly decomposes into the direct sum of global one-dimensional eigenspaces.

Keywords

eigenvalue, resolution, self-adjoint matrices, unitary group action

Mathematical Subject Classification 2010

Primary: 35P05

Secondary: 53C10

Milestones

Received: 12 August 2015

Revised: 29 June 2016

Accepted: 10 October 2016

Published: 8 April 2017