Algunas caracterizaciones y propiedades de pares de matrices conmutantes

Abstract

En este trabajo, se realiza un estudio de la dimensión del álgebra generada por dos matrices conmutantes mediante dos métodos diferentes; en el primero se usan herramientas del álgebra lineal y en el segundo se usan razonamientos de la geometría algebraica. Además, se realiza un estudio de la irreducibilidad de la variedad de m-uplas de matrices conmutantes de tamaño n x n para valores de m y n particulares. / Abstract. In this work, it was made a study of the dimension of the algebra generated by two commuting matrices by two different methods; the first one uses only tools of linear algebra and the other one bases its reasoning on elements of algebraic geometry. We also performed a study of the irreducibility of the variety of m-tuples of commuting n x n matrices for some values of m and n (Texto tomado de la fuente).

In this work, it was made a study of the dimension of the algebra generated by two commuting matrices by two different methods; the first one uses only tools of linear algebra and the other one bases its reasoning on elements of algebraic geometry. We also performed a study of the irreducibility of the variety of m-tuples of commuting n × n matrices for some values of m and n.