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Schur complement
Tool in linear algebra and matrix analysis
Schur complement
The Schur complement is a key tool in the fields of linear algebra, the theory of matrices, numerical analysis, and statistics. It is defined for a block matrix. Suppose p, q are nonnegative integers such that p + q > 0, and suppose A, B, C, D are respectively p × p, p × q, q × p, and q × q matrices of complex numbers. Let M = [ A B C D ] {\displaystyle M={\begin{bmatrix}A&B\\C&D\end{bmatrix}}} so that M is a (p + q) × (p + q) matrix. If D is invertible, then the Schur complement of the block D of the matrix M is the p × p matrix defined by M...
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