One derivation I was verifying holds true if:
$$Q^{-1}\left(Q^{-1}+P^{-1}\right)^{-1}P^{-1}=\left(Q+P\right)^{-1}$$
where Q and P are positive definite matrices.
I've done some numerical tests and I incline to believe that.
But, where does this come from? I could not derive it from Woodbury matrix identity.
