Suppose $\begin{bmatrix} K_{11} K_{12}\\K_{12}^T K_{22} \end{bmatrix}\sim\mathcal{IW}\left(\eta,\begin{bmatrix} \Sigma_{11} \Sigma_{12}\\\Sigma_{12}^T \Sigma_{22} \end{bmatrix}\right)$.

- What is the conditional distribution of $K_{11}|K_{22}$ and $K_{12}|K_{22}$
- What is the expectation of $K_{12}^TK_{22}^{-1}$