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The Schur complement of a block matrix, encountered in linear algebra and the theory of matrices, is defined as follows. Suppose p, q are nonnegative integers...

In numerical analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition...

after Issai Schur: List of things named after Issai Schur Schur algebra Schur complement Schur index Schur indicator Schur multiplier Schur orthogonality...

subspaces Orthogonal complement Schur complement Complement (complexity), relating to decision problems and complexity classes Complement operator (regular...

conjecture Schur complement method Schur complement Schur-convex function Schur decomposition Schur functor Schur index Schur's inequality Schur's lemma (from...

mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one...

{In} (H_{11})+\mathrm {In} (H/H_{11})} where H/H11 is the Schur complement of H11 in H: H / H 11 = H 22 − H 12 ∗ H 11 − 1 H 12 . {\displaystyle...

In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says...

are conformable with them for partitioning. Furthermore, A and the Schur complement of A in P: P/A = D − CA−1B must be invertible. Equivalently, by permuting...

proved with stronger conditions on the blocks, for instance, using the Schur complement. A general quadratic form f ( x ) {\displaystyle f(\mathbf {x} )} on...

G} has a complement in G {\displaystyle G} . Moreover if either N {\displaystyle N} or G / N {\displaystyle G/N} is solvable then the Schur–Zassenhaus...

matrix. The result is named after Issai Schur (Schur 1911, p. 14, Theorem VII) (note that Schur signed as J. Schur in Journal für die reine und angewandte...

triangularizable, see Schur decomposition Schur test for boundedness of integral operators Schur's theorem Schur's property Schur complement This disambiguation...

-j}=X_{j}^{T}X_{-j},r_{-j,j}=X_{-j}^{T}X_{j},r_{-j,-j}=X_{-j}^{T}X_{-j}} . By using Schur complement, the element in the first row and first column in r − 1 {\displaystyle...

decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula Matrix equivalence...

using either the Leibniz formula or a factorization involving the Schur complement, is det ( A 0 C D ) = det ( A ) det ( D ) = det ( A B 0 D ) . {\displaystyle...

matrix Σ ¯ {\displaystyle {\overline {\boldsymbol {\Sigma }}}} is the Schur complement of Σ22 in Σ. That is, the equation above is equivalent to inverting...

K Y | X {\displaystyle \operatorname {K} _{\mathbf {Y|X} }} is the Schur complement of K X X {\displaystyle \operatorname {K} _{\mathbf {XX} }} in Σ {\displaystyle...

) = {\displaystyle (D-CA^{-1}B)=} a much smaller matrix called the Schur complement of A {\displaystyle A} . This is the FKF method that may make it computationally...

worked in linear algebra and matrix theory. She gave the name to Schur complements and is the namesake of the Haynsworth inertia additivity formula....