Further results on the reverse-order law

DOI10.1016/0024-3795(79)90027-2zbMath0414.15006OpenAlexW2039317353MaRDI QIDQ599138

Nobuo Shinozaki, Masaaki Sibuya

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1016/0024-3795(79)90027-2

zbMATH Keywords

Moore-Penrose inversegeneralized inverse of a matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09)

Related Items (15)

Reverse order laws for least squares \(g\)-inverses and minimum norm \(g\)-inverses of products of two matrices ⋮ Forward order law for \(g\)-inverses of the product of two matrices ⋮ On the product of projectors and generalized inverses ⋮ Miscellaneous reverse order laws for generalized inverses of matrix products with applications ⋮ The product of operators with closed range and an extension of the reverse order law ⋮ 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 ⋮ Forward order law for the generalized inverses of multiple matrix product ⋮ Reverse order law for generalized inverses of multiple operator product ⋮ Mixed-type reverse-order laws for the generalized inverses of an operator product ⋮ Reverse order law of group inverses of products of two matrices ⋮ Mixed-type reverse order law of \((AB)^{(13)}\) ⋮ Equalities and inequalities for ranks of products of generalized inverses of two matrices and their applications ⋮ Various solutions to reverse order law problems ⋮ Reverse order law for reflexive generalized inverses of products of matrices

Cites Work

• The reverse order law \((AB)^-\) = \(B^-A^-\)
• Explicit solutions to the reverse order law \((AB)^+=B^-_{mr}A^-_{lr}\)
• Generalizations of the reverse order law with related results
• Note on the Generalized Inverse of a Matrix Product
• On the ``Reverse Order Law Related to the Generalized Inverse of Matrix Products
• An Extension of the Generalized Inverse of a Matrix
• The Pseudo-Inverse of a Product
• On Generalizations of the Reverse Order Law
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