The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\)

DOI10.1016/j.amc.2003.08.034zbMath1089.15007OpenAlexW1993134156MaRDI QIDQ1881692

Bing Zheng, Guo-rong Wang

Publication date: 14 October 2004

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.08.034

zbMATH Keywords

Drazin inverseMoore-Penrose inversegroup inverseMatrix productGeneralized inverse \(A_{T,S}^{(2)}\)rank identityReverse order law

Mathematics Subject Classification ID

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

Related Items (13)

Rank equalities related to the generalized inverse \(A^{(2)}_{T,S}\) with applications ⋮ The block independence in the generalized inverse \(A_{T,S}(2)\) for some ordered matrices and applications ⋮ Condensed Cramer rule for some restricted quaternion linear equations ⋮ Determinantal representation of the generalized inverses over the quaternion skew field with applications ⋮ 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 ⋮ Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field ⋮ The reverse order laws for {1, 2, 3}- and {1, 2, 4}-inverses of multiple matrix products ⋮ The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\) over a skew field ⋮ The forward order laws for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of multiple matrix products ⋮ Determinantal representations of the generalized inverses \(A_{T,S}^{(2)}\) over the quaternion skew field with applications ⋮ Various solutions to reverse order law problems ⋮ The mixed-type reverse order laws for weighted generalized inverses of a triple matrix product

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• Triple reverse-order law for weighted generalized inverses
• Reverse order laws for generalized inverses of multiple matrix products
• Inverse Order Rule for Weighted Generalized Inverse
• Note on the Generalized Inverse of a Matrix Product

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