Some generalized inverses of partition matrix and quotient identity of generalized Schur complement

DOI10.1016/j.amc.2007.05.050zbMath1140.15003OpenAlexW2135728501MaRDI QIDQ2474868

Xingping Sheng, Guo-Liang Chen

Publication date: 6 March 2008

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2007.05.050

zbMATH Keywords

linear systemDrazin inversegeneralized inverseMoore-Penrose inversegroup inverseblock matrixgeneralized Schur complementfirst Sylvester identityquotient identities

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24) Linear equations (linear algebraic aspects) (15A06)

Related Items (11)

On the inverse of a special Schur complement of an operator ⋮ Representations for the Drazin inverse of \(2\times 2\) block-operator matrix with singular Schur complement ⋮ Perturbation bound of the group inverse and the generalized Schur complement in Banach algebra ⋮ Drazin inverse of partitioned matrices in terms of Banachiewicz-Schur forms ⋮ Formulae for the generalized Drazin inverse of a block matrix in terms of Banachiewicz-Schur forms ⋮ Representations of the Moore–Penrose inverse for a class of 2-by-2 block operator valued partial matrices ⋮ Group inverse for block matrix with \(t\)-potent subblock ⋮ Representations of generalized inverses and Drazin inverse of partitioned matrix with Banachiewicz-Schur forms ⋮ Representations of the Drazin inverse on solution of a class singular differential equations ⋮ Expression of the Drazin and MP-inverse of partitioned matrix and quotient identity of generalized Schur complement ⋮ On Hermitian generalized inverses and positive semidefinite generalized inverses

Cites Work

• Unnamed Item
• Weighted generalized inverses of partitioned matrices in Banachiewicz-Schur form
• Generalized Schur-complements and a test for total positivity
• Other manifestations of the Schur complement
• Schur complements and statistics
• Matrix extrapolation algorithms
• The Schur complement and its applications
• Manifestations of the Schur complement
• Pseudo-Schur complements and their properties
• Some Schur complement identities and applications to matrix extrapolation methods
• A new proof of Haynsworth's quotient formula for Schur complements
• On Schur's complement
• Expressions for the drazin inverse of a 2×2 Block Matrix
• An Identity for the Schur Complement of a Matrix

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