Infinitesimal calculus MOC

Matrix calculus

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

Invertible matrix

Let 𝐌 :ℝ →GL𝑛⁡(ℂ) :𝑡 ↦𝑀(𝑡) be a 𝐶1-map.

1. 𝜕𝜕𝑡ln⁡|det𝐌|=tr⁡(𝐌−1𝜕𝐌𝜕𝑡)

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