A hermitian linear transformation must satisfy (|T) = (T|) for all vectors |) and |). Prove that

A hermitian linear transformation must satisfy (α|T̂β) = (T̂α|β) for all vectors |α) and |β). Prove that it is (surprisingly) sufficient that (ϒ|T̂ϒ) = (T̂ϒ|ϒ) for all vectors |ϒ).