The reverse order law for \(\{1, 3, 4\}\)-inverse of the product of two matrices

DOI10.1016/j.amc.2009.12.056zbMath1187.15005OpenAlexW2053191399MaRDI QIDQ961627

Deqiang Liu, Hu Yang

Publication date: 31 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.12.056

zbMATH Keywords

numerical examplesgeneralized inversePenrose equationsreverse order lawminimal ranksmaximal ranks

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (8)

Improvements on the reverse order laws ⋮ Applications of completions of operator matrices to reverse order law for \(\{1\}\)-inverses of operators on Hilbert spaces ⋮ Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law ⋮ Mixed-type reverse-order laws of \((AB)^{(1,2,3)}\) and \((AB)^{(1,2,4)}\) ⋮ A comment on some recent results concerning the reverse order law for \(\{ 1, 3, 4 \}\)-inverses ⋮ The forward order laws for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of multiple matrix products ⋮ Various solutions to reverse order law problems ⋮ Unnamed Item

Cites Work

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• Reverse order law for reflexive generalized inverses of products of matrices
• When is \(B^ -A^ -\) a generalized inverse of \(AB\)?
• Reverse order laws for the generalized inverses of multiple matrix products
• Reverse order laws for least squares \(g\)-inverses and minimum norm \(g\)-inverses of products of two matrices
• Equivalent conditions for generalized inverses of products
• A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications
• Generalized inverses. Theory and applications.
• Reverse order laws for generalized inverses of multiple matrix products
• On reverse-order laws for least-squares g-inverses and minimum norm g-inverses of a matrix product
• The representation of generalized inverse \(A_{T,S}^{(2,3)}\) and its applications
• More on maximal and minimal ranks of Schur complements with applications
• Further Results on the Reverse Order Law for Generalized Inverses
• Inverse Order Rule for Weighted Generalized Inverse
• Note on the Generalized Inverse of a Matrix Product

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