My Math Forum Operators exercise

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 December 26th, 2016, 03:54 PM #1 Member   Joined: Dec 2016 From: - Posts: 54 Thanks: 10 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!
 December 28th, 2016, 05:54 PM #2 Global Moderator   Joined: May 2007 Posts: 6,438 Thanks: 562 Something doesn't look right. If A and B are identity matrices, they satisfy the conditions, but the product is an identity matrix.
 December 29th, 2016, 07:48 AM #3 Member   Joined: Dec 2016 From: - Posts: 54 Thanks: 10 yes I know, that is why it looks odd to me...

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