1. The problem statement, all variables and given/known data Let V be a finite dimensional vector field over F. Let T:V→V Let c be a scalar and suppose there is v in V such that T(v)=cv, then show there exists a non-zero linear functional f on V such that Tt(f)=cf. Tt denotes T transpose. 2. Relevant equations Tt(f)=f°T. Ev(f)=f(v). Let V*=HomF(V,F) V*=(V*)* E:V→V** i.e. E(v)=Ev Theorem: E is an isomorphism iff V is finite dimensional 3. The attempt at a solution Ev(Tt(f))=f°T(v)=cf(v). But now I need to show there is f such that Tt(f)=cf, not just for specific v that satisfies T(v)=cv.