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December 26th, 2016, 03:54 PM   #1
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Operators exercise

Given two hermitian operators $A$ and $B$, both with positive eigenvalues, show that:

\begin{eqnarray}
\text {Tr}AB\geq 0
\end{eqnarray}

I have done this part of the exercise, but the second part says to show that accordingly then
\begin{eqnarray}
AB= 0
\end{eqnarray}
Where does this follow from? I cannot get a prove of this, some help please!
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December 28th, 2016, 05:54 PM   #2
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Something doesn't look right. If A and B are identity matrices, they satisfy the conditions, but the product is an identity matrix.
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December 29th, 2016, 07:48 AM   #3
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yes I know, that is why it looks odd to me...
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