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I recently posted a question here about adjoint maps. I now want to take this further and show that - with the assumptions as in the original - the minimum polynomials of $T$ and $T^{*}$ are the same. Further to this, what can be said of the eigenvalues of $T$ and $T^{*}$?

Any help would be appreciated. Best regards.

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This is false over $\mathbb{C}$. You need to specify that you're working over $\mathbb{R}$. –  Qiaochu Yuan Jan 12 '13 at 1:33
    
The question states that the inner product space is real. –  Mathmo Jan 12 '13 at 5:04
    
Questions on SE should be self-contained whenever possible. There's no need to make the reader refer to a different question to obtain a short list of hypotheses that is easy to state. –  Qiaochu Yuan Jan 12 '13 at 5:08

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