Abstract

MARMOLEJO, Miguel A.. Jordan form of the Fréchet derivative of matrix functions. Integración - UIS [online]. 2018, vol.36, n.1, pp.1-19. ISSN 0120-419X.  https://doi.org/10.18273/revint.v36n1-2018001.

In this paper we present a formula to evaluate matrix functions f: A ⊂ C2×2 → C2×2, in terms of two scalar functions that only depend on the trace and the determinant of X ∈ C2×2. 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) : C2×2 → C2×2 is given.

Keywords : Matrix function; Jordan canonical form; Fréchet derivative.

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