# Schur determinant lemma

A formula for the determinant of a matrix in block form. Let the $2n \times 2n$ matrix $M$ be partitioned into $n \times n$ blocks, $$M = \left({ \begin{array}{cc} P & Q \\ R & S \end{array} }\right) \ .$$
Then the determinant $$\det M = \det (PS - RQ) \ .$$