View source for Schur determinant lemma

{{MSC|15A15}}

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
$$
\det M = \det (PS - RQ) \ .
$$

====References====
* Zhang, Fuzhen (ed.) ''The Schur complement and its applications'', Numerical Methods and Algorithms '''4''' Springer (2005) {{ISBN|0-387-24271-6}} {{ZBL|1075.15002}}