Reverse order law for reflexive generalized inverses of products of matrices
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Publication:1307542
DOI10.1016/S0024-3795(97)10068-4zbMath0933.15008MaRDI QIDQ1307542
Musheng Wei, Alvaro Rodolfo de Pierro
Publication date: 19 December 1999
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
generalized inversesproduct singular value decompositionproduct of two matricesreflexive \(g\)-inverse
Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Eigenvalues, singular values, and eigenvectors (15A18)
Related Items (24)
The reverse order law for the generalized inverse \(A^{(2)}_{T,S}\) ⋮ 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 ⋮ Reverse order law of Drazin inverse for bounded linear operators ⋮ Improvements on the reverse order laws ⋮ Reverse order law for least squares g-inverses of multiple matrix products ⋮ 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 ⋮ The reverse order law for \(\{1, 3, 4\}\)-inverse of the product of two matrices ⋮ A note on the reverse order law for least squareg-inverse of operator product ⋮ Reverse order laws for reflexive generalized inverse of operators ⋮ Reverse order law of group inverses of products of two matrices ⋮ The reverse order laws for {1, 2, 3}- and {1, 2, 4}-inverses of multiple matrix products ⋮ Mixed-type reverse-order laws of \((AB)^{(1,2,3)}\) and \((AB)^{(1,2,4)}\) ⋮ The reverse order law for the \(W\)-weighted Drazin inverse of multiple matrices product ⋮ The forward order laws for \(\{1,2,3\}\)- and \(\{1,2,4\}\)-inverses of multiple matrix products ⋮ Moore-Penrose inverse in rings with involution ⋮ The reverse order laws for \(\{1,2,3\}\) - and \(\{1,2,4\}\) -inverses of a two-matrix product ⋮ Various solutions to reverse order law problems ⋮ The mixed-type reverse order laws for weighted generalized inverses of a triple matrix product ⋮ A note on the forward order law for least square \(g\)-inverse of three matrix products ⋮ Unnamed Item ⋮ The forward order laws for {1,2,3}- and {1,2,4}-inverses of a three matrix products
Cites Work
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- Further results on the reverse-order law
- A tree of generalizations of the ordinary singular value decomposition
- The reverse order law \((AB)^-\) = \(B^-A^-\)
- When is \(B^ -A^ -\) a generalized inverse of \(AB\)?
- Equivalent conditions for generalized inverses of products
- Computing the Singular Value Decomposition of a Product of Two Matrices
- Note on the Generalized Inverse of a Matrix Product
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