General expressions for the Moore-Penrose inverse of a 2\(\times 2\) block matrix

DOI10.1016/0024-3795(91)90351-VzbMath0723.15004MaRDI QIDQ757525

Jian-Ming Miao

Publication date: 1991

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Moore-Penrose inverseblock matrixpositive definite

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09)

Related Items (12)

New representations of the group inverse of \(2 \times 2\) block matrices ⋮ The Moore-Penrose inverses of \(m\times n\) block matrices and their applications ⋮ Representations for weighted Moore-Penrose inverses of partitioned adjointable operators ⋮ The numerical approximation of nonlinear functionals and functional differential equations ⋮ On Moore-Penrose inverses of quasi-Kronecker structured matrices ⋮ New representations of the Moore-Penrose inverse of \(2 \times 2\) block matrices ⋮ Expressions for the Moore-Penrose inverse of block matrices involving the Schur complement ⋮ Representations of generalized inverses and Drazin inverse of partitioned matrix with Banachiewicz-Schur forms ⋮ Expression of the Drazin and MP-inverse of partitioned matrix and quotient identity of generalized Schur complement ⋮ Rank equalities for submatrices in generalized inverse \(M_{T,S}^{(2)}\) of \(M\) ⋮ Tutorial on Hybridizable Discontinuous Galerkin (HDG) Formulation for Incompressible Flow Problems ⋮ Inverses of \(2\times 2\) block matrices

Cites Work

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• The Moore-Penrose inverse of a partitioned matrix \(M=\begin{pmatrix} D&D\\ B&C\end{pmatrix}\)
• Block generalized inverses
• The Moore-Penrose inverse of a bordered matrix
• Singular Value Decomposition and the Moore–Penrose Inverse of Bordered Matrices
• Generalized Inverse Formulas Using the Schur Complement
• Generalized Inverses of Partitioned Matrices
• Representations for the Generalized Inverse of a Partitioned Matrix
• Generalized Inverses and Ranks of Block Matrices
• Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses

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