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I wish to prove that T is diagonalizable iff for every eigenvector v of T, there is an eigenvector u of T^* such that <u, v> is not equal to 0.

I've been thinking about generalized eigenvectors, but have not really gotten anywhere.

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- Thread starter ughpleasenope
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I wish to prove that T is diagonalizable iff for every eigenvector v of T, there is an eigenvector u of T^* such that <u, v> is not equal to 0.

I've been thinking about generalized eigenvectors, but have not really gotten anywhere.

- #2

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The other direction is not immediately obviously true to me but sounds plausible, I'll sleep on it.

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Would you mind elaborating? I've struggled with this for a while.

The other direction is not immediately obviously true to me but sounds plausible, I'll sleep on it.

- #4

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What kind of basis of ##V^*## do you get from this? (I guess if your class is very matrix based this question might not make sense)

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