Infinitesimal calculus MOC

Matrix calculus

This Zettel is a collection of identities for infinitesimal calculus with matrices.

Invertible matrix

Let be a -map.

\frac{ \partial }{ \partial t } \ln \abs{\det \mathbf{M}} = \Tr \left( \mathbf{M}^{-1} \frac{ \partial \mathbf{M} }{ \partial t } \right)