Generalized inverse \(A^{(2)}_{T,S}\) and a rank equation

DOI10.1016/S0096-3003(03)00786-0zbMath1057.15008WikidataQ56660709 ScholiaQ56660709MaRDI QIDQ1883547

Bing Zheng, Ravindra B. Bapat

Publication date: 13 October 2004

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

zbMATH Keywords

characterizationDrazin inversegeneralized inverseMoore-Penrose inversegroup inverseouter inversematrix decompositionrank equation

Mathematics Subject Classification ID

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

Related Items (15)

Exploiting higher computational efficiency index for computing outer generalized inverses ⋮ Neural network approach to computing outer inverses based on the full rank representation ⋮ Higher-order convergent iterative method for computing the generalized inverse and its application to Toeplitz matrices ⋮ Computation of outer inverses of tensors using the QR decomposition ⋮ Modified SMS method for computing outer inverses of Toeplitz matrices ⋮ Full-rank representations of outer inverses based on the QR decomposition ⋮ Recurrent Neural Network for Computing Outer Inverse ⋮ Comments on some recent results concerning \(\{2,3\}\) and \(\{2,4\}\)-generalized inverses ⋮ An efficient computation of generalized inverse of a matrix ⋮ Composite outer inverses for rectangular matrices ⋮ A class of numerical algorithms for computing outer inverses ⋮ A note on the perturbation of an outer inverse ⋮ High-order iterative methods for the DMP inverse ⋮ Varying-parameter Zhang neural network for approximating some expressions involving outer inverses ⋮ Complex ZNN for computing time-varying weighted pseudo-inverses

Cites Work

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• A characterization of the Moore-Penrose inverse
• Perturbation bounds for the generalized inverses \(A_{T,S}^{(2)}\) with application to constrained linear system.
• On integral representation of the generalized inverse \(A_{T,S}^{(2)}\).
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• Characterization of generalized inverses by a rank equation.
• A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications
• A characterization for the \(W\)-weighted Drazin inverse and a Cramer rule for the \(W\)-weighted Drazin inverse solution
• The representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\)
• (T,S) splitting methods for computing the generalized inverse and rectangular systems^∗
• Generalizing the Singular Value Decomposition
• A Characterization and Representation of the Drazin Inverse
• On the perturbation and subproper splittings for the generalized inverse \(A_{T,S}^{(2)}\) of rectangular matrix \(A\)

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