On a class of non-Hermitian matrices with positive definite Schur complements
Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we sh...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/107578 |
| Acceso en línea: | http://hdl.handle.net/11336/107578 |
| Access Level: | acceso abierto |
| Palabra clave: | FRAMES KREIN SPACES COMPLEMENTO DE SCHUR OPERATOR DE CORTO-CIRCUITO https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Given a Hermitian matrices A∈C^n×n and D∈C^m×m, and k > 0, we characterize under which conditions there exists a matrix K∈C^n×m with ∥K∥ < k such that the non-Hermitian block-matrix [AK∗A−AKD] has a positive (semi-) definite Schur complement with respect to its submatrix A. Additionally, we show that K can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces. |
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