In linear algebra and the theory of matrices, the Schur complement of a matrix block (i.e., a submatrix within a larger matrix) is defined as follows. Suppose A, B, C, D are respectively p×p, p×q, q×p and q×q matrices, and D is invertible. Let
so that M is a (p+q)×(p+q) matrix.
Then the Schur complement of the block D of the matrix M is the p×p matrix
It is named after Issai Schur who used it to prove Schur's lemma, although it had been used previously. Emilie Haynsworth was the first to call it the Schur complement.
Read more about Schur Complement: Background, Application To Solving Linear Equations, Applications To Probability Theory and Statistics, Schur Complement Condition For Positive Definiteness
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