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Elsewhere on this site (link), Richard notes that \begin{equation} \Pi_{BL} = \frac{1}{2} \Pi + \frac{1}{2}Q, \end{equation} so long as we set $ P = I $ (where $I$ is the identity matrix) and $\Omega = \tau\Sigma$. This result seems relatively straightforward and intuitively obvious, but in trying to derive it I tend to end up with $\Pi_{BL} = \Pi + Q$.

Can someone provide a derivation? Or, at least, maybe sketch a proof so I can see what I might be missing? Thanks,

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