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espanolEn este articulo se presenta una formula para evaluar funciones matriciales f : A ⊂ C 2×2 → C 2×2, en terminos de dos funciones escalares que solo dependen de la traza y el determinante de X ∈ C 2×2 . Se explota el conocimiento de las derivadas de Frechet de las funciones traza y determinante para determinar la derivada de Frechet de f(·). Como resultado central, se da la forma canonica de Jordan de la derivada de Frechet Df(X) : C 2×2 → C 2×2. EnglishIn 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 Frechet derivatives of the trace and determinant functions is used to determine the Frechet derivative of f(·). As a central result, Jordan's canonical form of the Frechet derivative Df(X) : C 2×2 → C 2×2 is given.

Forma de Jordan de la derivada de Fréchet de funciones matriciales