Schur complement

Def)
Let $M=\begin{bmatrix} A & B \\ C & D \\ \end{bmatrix}$ where
$A: p \times p$ matrix, $B: p \times q$ matrix, $C: q \times p$ matrix, $D: q \times q$ matrix

If A is invertible, Schur Complement is $D-CA^{-1}B$
(If A is symmetric, Schure Complement is $D-B^T A^{-1} B$)

• Meaning of the form of Schure Complement
  

✔︎ If $M$ is positive definite, Schur Complement is also positive definite
pf)