Local extrema for Procustes problems in the set of positive definite matrices
Functional Analysis
2020-02-11 v1
Abstract
Given two positive definite matrices and , a well known result by Gelfand, Naimark and Lidskii establishes a relationship between the eigenvalues of and and those of 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}
}