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...

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

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

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

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...

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

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...

{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...

) = {\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...

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

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

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...

-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...

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...

}{\begin{pmatrix}0&0\\0&Q^{\frac {*}{2}}\end{pmatrix}},} where the Schur complement of A {\displaystyle {\begin{matrix}A\end{matrix}}} in the block matrix...

strategy is particularly advantageous if A is diagonal and D − CA−1B (the Schur complement of A) is a small matrix, since they are the only matrices requiring...

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

equivalent network with one less node. The equivalence follows from the Schur complement identity applied to the Kirchhoff matrix of the network. The equivalent...

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...

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...

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

differential equations as the capacitance matrix. Sherman–Morrison formula Schur complement Matrix determinant lemma, formula for a rank-k update to a determinant...

where S := B ∗ A − 1 B {\displaystyle S:=B^{*}A^{-1}B} denotes the Schur complement. Since S {\displaystyle S} is symmetric positive-definite, we can apply...

and Boyd, Edinburgh, fourth edition, 1939. Zhang, Fuzhen, ed. The Schur complement and its applications. Vol. 4. Springer Science & Business Media, 2006...

cosets of H. The Schur–Zassenhaus theorem guarantees the existence of complements of normal Hall subgroups of finite groups. Complements generalize both...

is the Fitting subgroup, and the Frobenius complement is uniquely determined up to conjugacy by the Schur-Zassenhaus theorem. In particular a finite group...

iteration for the iterative solution of the equations arising from the Schur complement method. This continuous iteration can be discretized by the finite...

Calculating the determinant of this matrix in two ways: direct and via Schur complement formula essentially gives Capelli's identity and its generalization...