On the Drazin inverse of block matrices and generalized Schur complement

DOI10.1016/J.AMC.2009.09.013zbMath1204.15013OpenAlexW2023341457MaRDI QIDQ1044446

J. Blot

Publication date: 18 December 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.09.013

zbMATH Keywords

Drazin inverseMoore-Penrose inversegroup inversegeneralized Schur complementcomplex block matricesBanaksiewicz-Schur form

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09)

Related Items (24)

Some formulas on the Drazin inverse for the sum of two matrices and block matrices ⋮ Generalizations of some conditions for Drazin inverses of the sum of two matrices ⋮ Representations for the Drazin inverses of \(2 \times 2\) block matrices ⋮ The Drazin inverse of the sum of two matrices and its applications ⋮ Representation for the generalized Drazin inverse of block matrices in Banach algebras ⋮ On Drazin inverse of operator matrices ⋮ On deriving the Drazin inverse of a modified matrix ⋮ Representation of the Drazin inverse for special block matrix ⋮ Several expressions for the generalized Drazin inverse of a block matrix in a Banach algebra ⋮ On additive properties of the Drazin inverse of block matrices and representations ⋮ Formulas for the Drazin inverse of matrices with new conditions and its applications ⋮ Representations for the Drazin inverse of \(2\times 2\) block-operator matrix with singular Schur complement ⋮ Further results on the group inverses and Drazin inverses of anti-triangular block matrices ⋮ Representations for the Drazin inverses of the sum of two matrices and some block matrices ⋮ On the generalized Drazin inverse in Banach algebras in terms of the generalized Schur complement ⋮ A representation for the Drazin inverse of block matrices with a singular generalized Schur complement ⋮ A note on computational formulas for the Drazin inverse of certain block matrices ⋮ The Drazin inverse of the sum of four matrices and its applications ⋮ A note on the formulas for the Drazin inverse of the sum of two matrices ⋮ A note on the formulas for the Drazin inverse of the sum of two matrices ⋮ Further results on the generalized Drazin inverse of block matrices in Banach algebras ⋮ Perturbation bound for the generalized Drazin inverse of an operator in Banach space ⋮ Some additive results for the Drazin inverse and its application ⋮ Expressions for the generalized Drazin inverse of a block matrix in a Banach algebra

Cites Work

• Unnamed Item
• A note on the representations for the Drazin inverse of \(2 \times 2\) block matrices
• The Schur complement and its applications
• Generalized inverses. Theory and applications.
• Formulas for the Drazin inverse of special block matrices
• Pseudo-Inverses in Associative Rings and Semigroups
• On the Generalized Drazin Inverse and Generalized Resolvent
• The Index and the Drazin Inverse of Block Triangular Matrices
• Expressions for the drazin inverse of a 2×2 Block Matrix
• Representations for the Drazin Inverse of a 2 x 2 Block Matrix
• Some additive results on Drazin inverse

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