Expectation value in terms of density matrix

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entropy1
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It says in Susskind's TM:

##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}##

with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
 
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Never mind, I see it now. Thanks.