Corollary 5

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

Let E be a vector space of finite dimension n. For every subspace F of E of dimension p, the orthogonal F' of F in E is of dimension n − p. For every subspace G' of E* of dimension q, the orthogonal G of G' in E is of dimension n − q and G' is the orthogonal of G in E*.

Theorem 7 gives another characterization of hyperplanes in E:

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

Cited by

Nothing.

Cites

Theorem 7