(See attached file for full problem description with symbols)
We have seen that the linear operator defined by is represented in the standard ordered basis by the matrix . This operator satisfies . Prove that if S is a linear operator on such that , then S = 0 or S = I, or these is an ordered basis for such that , A as defined above.
Hint: What are the possible values of
This is a proof regarding linear operators and the ordered basis.