Vol. 288, No. 1, 2017

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ISSN: 0030-8730
Eigenvalue resolution of self-adjoint matrices

Xuwen Zhu

Vol. 288 (2017), No. 1, 241–255
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
Authors
Xuwen Zhu
Department of Mathematics
Stanford University
380 Serra Mall
Stanford, CA 94305
United States