How do you get from the left hand side to the right hand side of this equation, this is converting the multivariate gaussian in to differential entropy.
$\mathbb{E}[(x-\mu)^T\Sigma^{-1}(x-\mu)]=\mathbb{E}[tr(x-\mu)^T\Sigma^{-1}(x-\mu)]$
How can we just put the trace in and remain equivalent?
Later on they pull the trace out of the expectation, does this mean that the trace is a linear operator and why?