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The Jacobian of the exponential function

Jan R. Magnus, Henk G.J. Pijls, Enrique Sentana
We derive closed-form expressions for the Jacobian of the matrix exponential function for both diagonalizable and defective matrices. The results are applied to two cases of interest in macroeconometrics: a continuoustime macro model and the parametrization of rotation matrices governing impulse response functions in structural vector autoregressions.
Year of publication:
[2020]
Authors: Magnus, Jan R. ; Pijls, Henk G. J. ; Sentana, Enrique
Publisher: Amsterdam, The Netherlands : Tinbergen Institute
Subject: Matrix differential calculus | Orthogonal matrix | Continuous-timeMarkov chain | Ornstein-Uhlenbeck process | Theorie | Theory | Lineare Algebra | Linear algebra | Analysis | Mathematical analysis | Stochastischer Prozess | Stochastic process
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