English

Local extrema for Procustes problems in the set of positive definite matrices

Functional Analysis 2020-02-11 v1

Abstract

Given two positive definite matrices AA and BB, a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of AA and BB and those of ABAB by means of majorization inequalities. In this work we make a local study focused in the spectrum of the matrices that achieve the equality in those inequalities. As an application, we complete some previous results concerning Procustes problems for unitarily invariant norms in the manifold of positive definite matrices.

Keywords

Cite

@article{arxiv.2002.03052,
  title  = {Local extrema for Procustes problems in the set of positive definite matrices},
  author = {Pablo Calderón and Noelia B. Rios and Mariano A. Ruiz},
  journal= {arXiv preprint arXiv:2002.03052},
  year   = {2020}
}