Conditional covariance: the Schur complement $\Sigma_{11}-\Sigma_{12}\Sigma_{22}^{-1}\Sigma_{21}$

Let $\underline X\sim N_p(\underline\mu,\Sigma)$ be partitioned into $\underline X^{(1)}$ ($q$ components) and $\underline X^{(2)}$ ($p-q$ components), with $\underline\mu$ and $\Sigma$ partitioned accordingly. Then the variance covariance matrix of the conditional distribution of $\underline X^{(1)}$ given $\underline X^{(2)}$ is: