The inertia of the symmetric approximation for low-rank matrices
© 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations. A usual situation occurs when a matrix obtained from experimental or simulated data is needed to be approximated by a matrix that lies in a co...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/111318 |
| Acceso en línea: | https://hdl.handle.net/2117/111318 https://dx.doi.org/10.1080/03081087.2017.1398710 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebras, Linear Matrices inertia indices positive definiteness rank approximation Symmetric matrices Àlgebra lineal Matrius (Matemàtica) Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Sumario: | © 2017 Informa UK Limited, trading as Taylor & Francis Group In many areas of applied linear algebra, it is necessary to work with matrix approximations. A usual situation occurs when a matrix obtained from experimental or simulated data is needed to be approximated by a matrix that lies in a corresponding statistical model and satisfies some specific properties. In this short note, we focus on symmetric and positive-semidefinite approximations and we show that the positive and negative indices of inertia of the symmetric approximation and the rank of the positive-semidefinite approximation are always bounded from above by the rank of the original matrix. |
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