Corollary 1

Tag 05T3, permanent. Cite it as [Bourbaki, Tag 05T3].

Let E and F be two vector spaces over a field K; the canonical mapping

E^* \otimes_K F \to \operatorname{Hom}_K(E, F)

(§ 4, no. 2, formula (11)) is injective; it is bijective when E or F is finite-dimensional.

This is a special case of Proposition 16 (i).

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

Cited by

Nothing.