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Ordered basis proof

(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


Solution Summary

This is a proof regarding linear operators and the ordered basis.