Forma de Jordan de la derivada de Fréchet de funciones matriciales

• Autores: Miguel A. Marmolejo L.
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 36, Nº. 1, 2018 (Ejemplar dedicado a: Revista Integración, temas de matemáticas), págs. 1-19
• Idioma: español
• DOI: 10.18273/revint.v36n1-2018001
• Títulos paralelos:
  • Jordan form of the Fréchet derivative of matrix functions
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• Resumen
  • español

    En este artículo se presenta una fórmula para evaluar funciones matriciales f : A ⊂ C 2×2 → C 2×2, en términos de dos funciones escalares que sólo dependen de la traza y el determinante de X ∈ C 2×2 . Se explota el conocimiento de las derivadas de Fréchet de las funciones traza y determinante para determinar la derivada de Fréchet de f(·). Como resultado central, se da la forma canónica de Jordan de la derivada de Fréchet Df(X) : C 2×2 → C 2×2.

  • English

    In this paper we present a formula to evaluate matrix functions f : A ⊂ C 2×2 → C 2×2, in terms of two scalar functions that only depend on the trace and the determinant of X ∈ C 2×2 . The knowledge of the Fréchet derivatives of the trace and determinant functions is used to determine the Fréchet derivative of f(·). As a central result, Jordan's canonical form of the Fréchet derivative Df(X) : C 2×2 → C 2×2 is given.

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