Group inverse for a class \(2\times 2\) block matrices over skew fields

DOI10.1016/j.amc.2008.05.145zbMath1159.15003OpenAlexW2088248122MaRDI QIDQ2378891

Changjiang Bu, Jiemei Zhao, Jinshan Zheng

Publication date: 14 January 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.05.145

zbMATH Keywords

Drazin inverserankgroup inverseskew fieldidempotent matrixblock matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (25)

RESULTS ON BUILDING FRACTIONAL MATRIX DIFFERENTIAL EQUATION SYSTEMS USING A CLASS OF BLOCK MATRICES ⋮ The representation of the Drazin inverse of anti-triangular operator matrices based on resolvent expansions ⋮ Group inverse for block matrices and some related sign analysis ⋮ On the group invertibility of operators ⋮ New representations of the group inverse of \(2 \times 2\) block matrices ⋮ Characterizations of the group invertibility of a matrix revisited ⋮ Representation of the Drazin inverse for special block matrix ⋮ The Drazin inverse of the linear combinations of two idempotents in the Banach algebra ⋮ Group inverses of matrices over right Ore domains ⋮ Further results on the group inverses and Drazin inverses of anti-triangular block matrices ⋮ Representations for the group inverse of anti-triangular block operator matrices ⋮ Group inverses for a class of \(2{\times}2\) block matrices over rings ⋮ ON THE GROUP INVERSE FOR THE SUM OF MATRICES ⋮ The \((2,2,0)\) Drazin inverse problem ⋮ The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\) over a skew field ⋮ A note on the group inverse of some \(2 \times 2\) block matrices over skew fields ⋮ The \((2,2,0)\) group inverse problem ⋮ Some results on the group inverse of the block matrix with a sub-block of linear combination or product combination of matrices over skew fields ⋮ Group inverse for block matrix with \(t\)-potent subblock ⋮ Group inverse for a class of \(2\times 2\) anti-triangular block matrices over skew fields ⋮ Group inverse for two classes of \(2\times 2\) anti-triangular block matrices over right Ore domains ⋮ Group inverse for the block matrices with an invertible subblock ⋮ The group invertibility of the product of two matrices over ring and its applications ⋮ Further results on the group inverse of some anti-triangular block matrices ⋮ Representations of the Drazin inverse on solution of a class singular differential equations

Cites Work

• Condition number for the Drazin inverse and the Drazin-inverse solution of singular linear system with their condition numbers
• Representations of the Drazin inverse for a class of block matrices
• A Note on Preconditioning Nonsymmetric Matrices
• Representations of the group inverse of some 2 x 2 block matrices
• On Solving Block-Structured Indefinite Linear Systems
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