Bourbaki

Corollary 1

Tag 05T7, permanent. Cite it as [Bourbaki, Tag 05T7].

Algebra, chapter II, § 7. Vector spaces

The rank of u is the smallest integer s such that there exists an expression u=∑i=1sxi⊗yiu = \sum_{i=1}^s x_i \otimes y_i, where xi∈Ex_i \in E and yi∈Fy_i \in F for 1≤i≤s1 \leq i \leq s.

This follows immediately from Proposition 17 and no. 2, Proposition 1.

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

Cited by

Nothing.

Cites

Transcribed from the printed edition, 1998, Springer. Not translated.