The bundle of simultaneously diagonalizable n-tuples of matrices
In this paper, a review of the simultaneous diagonalization of n-tuples of matrices for its applications in sciences is presented. For example, in quantum mechanics, position and momentum operators do not have a shared base that can represent the states of the system because they not commute, which...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:2117/188037 |
| Acceso en línea: | https://hdl.handle.net/2117/188037 https://dx.doi.org/10.37394/23206.2020.19.21 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic geometry Diagonalization Simultaneous diagonalization Bundles Geometria algebraica Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | In this paper, a review of the simultaneous diagonalization of n-tuples of matrices for its applications in sciences is presented. For example, in quantum mechanics, position and momentum operators do not have a shared base that can represent the states of the system because they not commute, which is why switching operators form a key element of quantum physics since they define quantities that are compatible, that is, defined simultaneously. We are going to study this kind of family of linear operators using geometric constructions such as the principal bundles and associating them with a cohomology class measuring the deviation of the local product structure from the global product structure. |
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