Schur determinant lemma

2020 Mathematics Subject Classification: Primary: 15A15 [MSN][ZBL]

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