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.
E:V→V** i.e. E(v)=Ev
Theorem: E is an isomorphism iff V is finite dimensional
The Attempt at a Solution
But now I need to show there is f such that Tt(f)=cf, not just for specific v that satisfies T(v)=cv.