Matrix calculus

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

Invertible matrix

Let $𝐌 : ℝ \to G L 𝑛 (ℂ) : 𝑡 \mapsto 𝑀 (𝑡)$ be a $𝐶 1$ -map.

𝜕 𝜕 𝑡 l n | d e t 𝐌 | = t r (𝐌 - 1 𝜕 𝐌 𝜕 𝑡)

Proof

proof