Schur complement

Summary

The Schur complement of an invertible block $A$ in a block matrix $\begin{pmatrix} A & B \\ C & D \end{pmatrix}$ is the matrix $D - C A^{-1} B$. It is what remains of the block $D$ after block Gaussian elimination removes the block $C$. It gives the determinant via the Schur complement, formulas for the inverse of a block matrix, and tests for positive definiteness.