Examinando por Materia "Forma canónica de Jordan"

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    Teorema de descomposición de módulos sobre dominios de ideales principales
    (2020-06-10) Arteaga Genes, Lina Paola; Guzmán Navarro, Ricardo Miguel
    In this work an introductory study of module theory is made. A module is a structure defined analogously to a vectorial space but replacing the field by a ring. First, we provide some definitions, notations, and key necessary results which are going to help us with the understanding of the structure of finite generated modules (F.G.M) over a principal ideal domain (P.I.D). The focus of this project is the study of module theory, principally by using tools like ring theory and group theory. Finally, an application of the module decomposition theorem over P.I.D. to the Jordan and rational normal forms is presented, i.e. we are going to establish a connection between an important theorem of module theory and some linear algebra structures.
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    PublicaciónAcceso abierto
    Vectores propios generalizados y forma canónica de Jordan
    (2020-06-10) Castro Martínez, Paola Andrea; Guzmán Navarro, Ricardo Miguel
    In this work, generalized eigenvalues are used to study the Jordan normal form and some applications of this are shown. We prove that C n can be decomposed as a direct sum of generalized proper subspaces by using annihilating polynomials and the minimal polynomial. We also prove that each generalized eigensubspace can be decomposed as a direct sum of Jordan cyclic subspaces. Finally, the Jordan Theorem is proved by using the above decompositions.