Lie groups and Lie algebras Optional Extra: Any torus is contained in a maximal torus

We prove that any torus is contained in a maximal torus, which completes our proof that nontrivial maximal tori exist in compact groups. This video is optional.

[@TheDarktsun]

8:37 I'm not 100% sure but I think it might be that iλ∈(i Lie(T))* since λ:Lie(T)->ℝ but I might be being overly pedantic by pointing that out.