Results 11 to 20 of about 567 (182)
Six generalized Schur complements
Linear Algebra and its Applications, 1988 The authors give a unified treatment of equivalence between some old and new generalizations of the Schur complement of matrices.
Butler, C.A., Morley, T.D.
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Some inequalities on generalized Schur complements
Linear Algebra and its Applications, 1999 Let \(A=[A_{ij}]\) denote a block matrix of order two with square diagonal blocks. The generalized Schur complement \(S_1(A)\) of \(A_{11}\) is defined by \(S_1(A)=A_{22} -A_{21}A^+_{11} A_{12}\) where \(A^+_{11}\) denotes the Moore-Penrose pseudoinverse of \(A_{11}\) so that \(S_1(A)\) is defined also for singular matrices. For a Hermitian matrix \(A\)
Wang, Bo-Ying +2 more
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Linear Algebra and its Applications, 1979 AbstractLet A be an n×n complex matrix. For a suitable subspace M of Cn the Schur compression A M and the (generalized) Schur complement A/M are defined. If A is written in the form A= BCST according to the decomposition Cn=M⊕M⊥ and if B is invertible, then AM=BCSSB−1C and A/M=000T−SB−1C· The commutativity rule for Schur complements is proved: (A/M)/N=(
Ando, T.
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Generalized Schur complements and P-complementable operators [PDF]
Linear Algebra and its Applications, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Massey, Pedro Gustavo +1 more
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The Schur complements of generalized doubly diagonally dominant matrices
Linear Algebra and its Applications, 2004 It is known that the Schur complements of diagonally dominant matrices are diagonally dominant, and that the same is true for doubly diagonally dominant matrices. In this paper, the authors extend these results to the generalized doubly diagonally dominant matrices (a proper subset of H-matrices); that is, they show that the Schur complement of a ...
Liu, Jianzhou +2 more
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The Reverse Order Law for the {1,3M,4N}—The Inverse of Two Matrix Products
AxiomsBy using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law (AB){1,3M,4K}=B{1,3N,4K}A{1,3M,4N} are presented.
Yingying Qin, Baifeng Qiu, Zhiping Xiong
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Some Results on the Drazin Inverse of a Modified Matrix with New Conditions
International Journal of Analysis and Applications, 2014 In this article, we consider representations of the Drazin inverse of a modified matrix M = A−CDdB with the generalized Schur complement Z = D − BAdC under different conditions given in recent articles on the subject.
Abdul Shakoor, Hu Yang, Ilyas Ali
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International Journal of Robust and Nonlinear Control, EarlyView., 2023 Abstract We propose a hierarchical energy management scheme for aggregating Distributed Energy Resources (DERs) for grid flexibility services. To prevent a direct participation of numerous prosumers in the wholesale electricity market, aggregators, as self‐interest agents in our scheme, incentivize prosumers to provide flexibility. We firstly model the
Xiupeng Chen +3 more
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Forward Order Law for the Reflexive Inner Inverse of Multiple Matrix Products
Axioms, 2022 The generalized inverse has numerous important applications in aspects of the theoretic research of matrices and statistics. One of the core problems of generalized inverse is finding the necessary and sufficient conditions for the reverse (or the ...
Wanna Zhou, Zhiping Xiong, Yingying Qin
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Forces in Mechanics, 2022 We recently demonstrated the reduction of the unified continuum and variational multiscale formulation to a computationally efficient fluid-structure interaction (FSI) formulation via three modeling assumptions pertaining to the vascular wall. Similar to
Ingrid S. Lan +3 more
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