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Quiz dossier / The Matrix Cookbook

02 - Derivatives

Advanced formula selection, assumption checking, and exact application for Derivatives, book pages 8-16.

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Question 1

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Differential rulebook

Treat AA as constant.

ValidInvalidStatement
d(XY)=(dX)Y+X(dY)d(XY)=(dX)Y+X(dY)
d(X−1)=X−1(dX)X−1d(X^{-1})=X^{-1}(dX)X^{-1}
d lndetX=Tr(X−1dX)d\,ln det X=Tr(X^{-1}dX)
d(X⊗Y)=dX⊗Y+X⊗dYd(X\otimes Y)=dX\otimes Y+X\otimes dY