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Ordered basis proof

(See attached file for full problem description with symbols)

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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

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Solution Summary

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

$2.19