A proof of the Cayley-Hamilton theorem using algebraic geometry

• Autores: Mejía Alemán, Carlos, Núñez Rodriguez, Irene Edith, Gálvez Pérez, Rodolfo José, Pino Romero, Neisser
• Formato: artículo
• Fecha de Publicación: 2021
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/3971
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3971
• Nivel de acceso: acceso abierto
• Materia: Espacio afín; conjunto algebraico; variedad algebraica; Espacio afín, conjunto algebraico, variedad algebraica, topología de Zariski.; Affine space; algebraic set; algebraic manifold; Zariski topology

In this work, we will prove the Cayley-Hamilton theorem using algebraic geometry. We will see a different proof than the one seen in a linear algebra course, in this case we will use the Zariski topology, then we will take advantage of the fact that every square matrix of order n _ n, with entries in a field K, denoted by (aij)n_n can be seen as an element of the affine space of dimension n _ n over the field K and thanks to this, we can resort to algebraic sets and algebraic varieties in order to obtain some results seen in an algebraic geometry and to get a proof of the Cayley-Hamilton theorem.