Concrete minimal 3 × 3 Hermitian matrices and some general cases

Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.

Detalhes bibliográficos
Autores: Klobouk, Abel H., Varela, Alejandro
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/46235
Acesso em linha:http://hdl.handle.net/11336/46235
Access Level:acceso abierto
Palavra-chave:MINIMAL HERMITIAN MATRIX
DIAGONAL MATRIX
QUOTIENT OPERATOR NORM
BEST APROXIMATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:Given a Hermitian matrix M ∈ M3(ℂ) we describe explicitly the real diagonal matrices DM such that ║M + DM║ ≤ ║M + D║ for all real diagonal matrices D ∈ M3(ℂ), where ║ · ║ denotes the operator norm. Moreover, we generalize our techniques to some n × n cases.