Remark

Tag 0AUJ, permanent. Cite it as [Bourbaki, Tag 0AUJ].

Lie Groups and Lie Algebras, chapter VI, § 1. Root systems

Choose a scalar product on $V_R$ invariant under $W(R)$ . It is then possible to speak of the length of a root and the angle between two roots. Prop. 7 shows that this angle is independent of the choice of scalar product, as is the ratio of the lengths of two roots, provided they belong to the same irreducible component of $R$ .

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

Cited by

Nothing.

Cites

Prop. 7