Local Lidskii's theorems for unitarily invariant norms

Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain orbits of matrices (under the action of the unitary group)....

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Detalles Bibliográficos
Autores principales: Massey, Pedro Gustavo, Rios, Noelia Belén, Stojanoff, Demetrio
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2018
Materias:
Matemática
Frame operator distance
Lidskii's inequality
Majorization
Unitarily invariant norms
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99883
https://ri.conicet.gov.ar/11336/88407
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-99883
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Frame operator distance
Lidskii's inequality
Majorization
Unitarily invariant norms
spellingShingle Matemática
Frame operator distance
Lidskii's inequality
Majorization
Unitarily invariant norms
Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
Local Lidskii's theorems for unitarily invariant norms
topic_facet Matemática
Frame operator distance
Lidskii's inequality
Majorization
Unitarily invariant norms
description Lidskii's additive inequalities (both for eigenvalues and singular values) can be interpreted as an explicit description of global minimizers of functions that are built on unitarily invariant norms, with domains consisting of certain orbits of matrices (under the action of the unitary group). In this paper, we show that Lidskii's inequalities actually describe all global minimizers of such functions and that local minimizers are also global minimizers. We use these results to obtain partial results related to local minimizers of generalized frame operator distances in the context of finite frame theory.
format Articulo
Preprint
author Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_facet Massey, Pedro Gustavo
Rios, Noelia Belén
Stojanoff, Demetrio
author_sort Massey, Pedro Gustavo
title Local Lidskii's theorems for unitarily invariant norms
title_short Local Lidskii's theorems for unitarily invariant norms
title_full Local Lidskii's theorems for unitarily invariant norms
title_fullStr Local Lidskii's theorems for unitarily invariant norms
title_full_unstemmed Local Lidskii's theorems for unitarily invariant norms
title_sort local lidskii's theorems for unitarily invariant norms
publishDate 2018
url http://sedici.unlp.edu.ar/handle/10915/99883
https://ri.conicet.gov.ar/11336/88407
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