Results 111 to 120 of about 408 (148)
A generalized Schur complement for nonnegative operators on linear spaces [PDF]
Banach Journal of Mathematical Analysis, 2018 Extending the corresponding notion for matrices or bounded linear operators on a Hilbert space we define a generalized Schur complement for a non-negative linear operator mapping a linear space into its dual and derive some of its properties.
L Klotz
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On the Drazin inverse of block matrices and generalized Schur complement
Applied Mathematics and Computation, 2009Different expressions are well-known for the Banaksiewicz-Schur form of a matrix involving the Moore-Penrose inverse, the group inverse or the Drazin inverse. In all of these cases, the generalized Schur complement (considering the corresponding Moore-Penrose, group or Drazin block) plays an important role.
N Castro-González
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Block idempotent matrices and generalized Schur complement
Applied Mathematics and Computation, 2007Given a matrix partitioned into \(2\times 2\) blocks, where the left upper block is a nonsingular matrix denoted as \(A\). The paper deals with the idempotency of the generalized Schur complement with a generalized inverse \(A^{(2)}_{T,S}\), where \(A^{(2)}_{T,S}\) denotes the {2}-inverse of \(A\) with range \(T\) and null space \(S\).
Jinhua Zhou, Guorong Wang
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On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement
Applied Mathematics and Computation, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E Dopazo, J Robles
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Some generalized inverses of partition matrix and quotient identity of generalized Schur complement
Applied Mathematics and Computation, 2008The authors initially extend the notion of the generalized Schur complement and study the expression of the Moore-Penrose inverse of \(2\times 2\) block matrices. Then, they propose expressions of the group inverse and the Drazin inverse for a block matrix under some conditions.
Xingping Sheng
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General H-matrices and their Schur complements
Frontiers of Mathematics in China, 2014This paper presents an extensive fully theoretical study of properties of generalized \(H\)-matrices. It is known, that \(H\)-matrices can be divided into three disjoint sets -- the invertible class \(H^I\), the singular class \(H^S\) and the mixed class \(H^M\).
Zhang, Cheng-Yi +3 more
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Generalized Inverse Formulas Using the Schur Complement
SIAM Journal on Applied Mathematics, 1974A formula for various generalized inverses of a partitioned complex matrix is established under certain general conditions. The use of this formula in obtaining the Moore–Penrose inverse of an arbitrary complex matrix is discussed.
Burns, Fennell +3 more
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A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse
SIAM Journal on Applied Mathematics, 1974Suppose the complex matrix M is partitioned into a $2 \times 2$ array of blocks; let $M_{11} = A,M_{12} = B,M_{21} = C,M_{22} = D$. The generalized Schur complement of A in M is defined to be $M/A = D - CA^ + B$, where $A^ + $ is the Moore–Penrose inverse of A. The relationship of the ranks of M, A, and $M/A$ is determined.
Carlson, David +2 more
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Inner Formulation of Lyapunov Stability Test and Generalized Schur-Complement
IFAC Postprint Volumes IPPV / International Federation of Automatic Control, 1981Abstract It is shown in this paper that for the stability condition of ẋ = Ax and x k = AX k-1 there exists a positive innerwise matrix, such that Q is a negative semi-innerwise matrix p. The inner formulation is shown for Hermite, reduced Hermite, Schur-Cohn and reduced Schur-Cohn criteria, and other criteria related to root-clustering problems ...
E I Jury, O Huseyin
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