# Von neumann entropy, log(P) ?

## Main Question or Discussion Point

Let P be a density matrix. Then the von neumann entropy is defined as
S(P) = -tr(P*log(P))

But how is log(P) defined ?

--edit--
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.

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$$ln(P) = -\sum_{n=1}^\infty \frac{1}{n}(I-A)^n$$

trosten said:
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
right. Usually easier by the way !

dextercioby
$$S:=-k\langle \ln\hat{\rho}\rangle_{\hat{\rho}}$$