# Schur determinant lemma

From Encyclopedia of Mathematics

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

**How to Cite This Entry:**

Schur determinant lemma.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Schur_determinant_lemma&oldid=54383