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.
| Autores: | , |
|---|---|
| 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 |
| 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. |
|---|