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eigenvalues

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Assume that T and U are linear operators on R^3, that UT = -TU and that UT has three distinct eigenvalues. Prove that one of the eigenvalues must be zero. (Hint: do the proof by contradiction: Assume the hypotheses and assume that none of the eigenvalues are zero. UT is one to one and therefore T is one to one.)

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This solution helps explore the concept of eigenvalues.

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