Corollary 3

Tag 0769, permanent. Cite it as [Bourbaki, Tag 0769].

Algebra, chapter VII, § 5. Endomorphisms of vector spaces

For each integer $s \geq 0$ we have $\operatorname{Tr}(u^s) = \sum_{i=1}^n \alpha_i^s$ . This formula is also valid for $s < 0$ provided $u$ is invertible.

This is a special case of the previous corollary.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Corollary 4, § 5
Lemma 2, Appendix 2

Cites

Nothing.