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I've come accross the identity det(expA)=exp(Tr(A)) many times now, but recently came across log(detA)=Tr(log(A)), can anyone explain to me why this is true? or if it can be derived from the more familiar first identity?

I'm not sure if there are any particular constraints the matrix must satisfy for the identity, it was a field theory book in which I saw it, so I guess the author could be assuming a couple of things about the matrices (maybe unitary for example)

cheers