A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications

From MaRDI portal
Publication:1808943

DOI10.1016/S0024-3795(98)00008-1zbMath0934.15003OpenAlexW2077639421MaRDI QIDQ1808943

Yi-Min Wei

Publication date: 29 April 2000

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(98)00008-1




Related Items (only showing first 100 items - show all)

A new representation for \(A_{T, S}^{(2, 3)}\)Generalized inverse \(A^{(2)}_{T,S}\) and a rank equationThe iterative methods for computing the generalized inverse \(A^{(2)}_{T,S}\) of the bounded linear operator between Banach spacesInnovation based on Gaussian elimination to compute generalized inverse \(A_{T,S}^{(2)}\)Rank equalities related to the generalized inverse \(A^{(2)}_{T,S}\) with applicationsOuter-star and star-outer matricesA family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrixRepresentations and computations of \(\{2, 3^\sim \}\) and \(\{2, 4^\sim \}\)-inverses in indefinite inner product spacesThe block independence in the generalized inverse \(A_{T,S}(2)\) for some ordered matrices and applicationsNote on the iterative methods for computing the generalized inverse over Banach spacesInterpolation algorithm of Leverrier-Faddev type for polynomial matricesRepresentation and approximate for generalized inverse \(A_{T,S}^{(2)}\): revisitedThree limit representations of the core-EP inverseFurther results on the reverse order law for \(\{1,3\}\)-inverse and \(\{1,4\}\)-inverse of a matrix productCharacterizations of the core inverse and the core partial orderingA note on condition numbers for generalized inverse \(A^{(2)}_{T,S}\) and constrained linear systemsApproximation of inverse operators by a new family of high-order iterative methodsA family of iterative methods for computing Moore-Penrose inverse of a matrixAn efficient method for computing the outer inverse \(A_{T,S}^{(2)}\) through Gauss-Jordan eliminationThe Generalized Inverse A(2)T, Sof a Matrix Over an Associative RingComputation of outer inverses of tensors using the QR decompositionThe representations and computations of generalized inverses \(A^{(1)}_{T,S}\), \(A^{(1,2)}_{T,S}\) and the group inverseCondition number related with generalized inverse \(A_{T,S}^{(2)}\) and constrained linear systemsCondensed Cramer rule for some restricted quaternion linear equationsThe representation and approximation of the \(W\)-weighted Drazin inverse of linear operators in Hilbert space.New proofs of two representations and minor of generalized inverse \(A_{T,S}^{(2)}\)Adjoints of a matrixA note on the representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\)Symbolic computation of \(A_{T,S}^{(2)}\)-inverses using QDR factorizationSome block matrices with signed Drazin inversesAn analog of the adjugate matrix for the outer inverse \(A^{(2)}_{T, S}\)On convergents infinite products and some generalized inverses of matrix sequencesSeveral representations of generalized inverse and their applicationRepresentations and properties of theW-Weighted Drazin inverseDeterminantal representation of the generalized inverses over the quaternion skew field with applicationsRecurrent Neural Network for Computing Outer InverseConditions for existence, representations, and computation of matrix generalized inversesCharacterization of generalized inverses by a rank equation.The generalized inverse over commutative ringsThe quasi-linear operator outer generalized inverse with prescribed range and kernel in Banach spacesOuter and (b,c) inverses of tensorsCharacterizations and representations of the \((P, Q)\)-outer generalized inverseThe iterative methods for \(A^{(2)}_{T,S}\) of the bounded linear operator between Banach spacesExistence criteria and expressions of the \((b,c)\)-inverse in rings and their applicationsPCR algorithm for parallel computing the solution of the general restricted linear equationsThe representation and computation of generalized inverse \(A^{(2)}_{T,S}\)The representation and approximation for the weighted Minkowski inverse in Minkowski space(T,S) splitting methods for computing the generalized inverse and rectangular systemsFull-rank representation of generalized inverse \(A_{T,S}^{(2)}\) and its applicationA class of numerical algorithms for computing outer inversesMatrix left symmetry factor and its applications in generalized inverses \(A_{T,S}^{(2,4)}\)The reverse order law for \(\{1, 3, 4\}\)-inverse of the product of two matricesRank equalities related to outer inverses of matrices and applicationsFurther results on iterative methods for computing generalized inversesExplicit expressions of the generalized inverses and condensed Cramer rulesExtension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrixAn efficient method to compute different types of generalized inverses based on linear transformationRank equalities related to the generalized inverses \(A_{T,S}^{(2)}\), \(B_{T_1,S_1}^{(2)}\) of two matrices \(A\) and \(B\)Condition numbers for the outer inverse and constrained singular linear systemCramer rule for the unique solution of restricted matrix equations over the quaternion skew fieldThe representations of generalized inverses of lower triangular operatorsHigher-order convergent iterative method for computing the generalized inverse over Banach spacesA geometrical approach on generalized inverses by Neumann-type seriesRepresentations of the Moore–Penrose inverse for a class of 2-by-2 block operator valued partial matricesCompute limλ → 0XIp+YAX)−1Yby the product singular value decompositionOn the perturbation and subproper splittings for the generalized inverse \(A_{T,S}^{(2)}\) of rectangular matrix \(A\)Determinantal representations of the generalized inverses \(A_{T,S}^{(2)}\) over the quaternion skew field with applicationsOn the Generalized Drazin Inverse and Generalized ResolventThe Representation and Computational Procedures for the Generalized Inverse of an OperatorAin Hilbert SpacesCharacterizations of k-commutative equalities for some outer generalized inversesA note on the perturbation of an outer inverseSuccessive matrix squaring algorithm for computing outer inversesThe representation of generalized inverse \(A_{T,S}^{(2,3)}\) and its applicationsOn the \((p,q)\) outer generalized inverse in Banach algebraA higher order iterative method for \(A^{(2)}_{T,S}\)Characterizations and representations of outer inverse for matrices over a ringThe Moore–Penrose inverses of lower triangular operatorsTwo closed novel formulas for the generalized inverse \(A_{T,S}^{(2)}\) of a complex matrix with given rankAn efficient class of iterative methods for computing generalized outer inverse \({M_{T,S}^{(2)}}\)The Drazin inverse in an arbitrary semiringUnnamed ItemDeterminantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applicationsCentralizer's applications to the \((b, c)\)-inverses in ringsRank equalities for submatrices in generalized inverse \(M_{T,S}^{(2)}\) of \(M\)The reduced minimum modulus of Drazin inverses of linear operators on Hilbert spacesA fast convergent iterative solver for approximate inverse of matricesThe representation and characterization of Drazin inverses of operators on a Hilbert spaceCondition number related to the outer inverse of a complex matrixA high-order iterate method for computing \(A_{T, S}^{(2)}\)Rank equalities related to the generalized inverses \(A^{\Vert (B_1,C_1)}\), \(D^{\Vert(B_2,C_2)}\) of two matrices \(A\) and \(D\)Varying-parameter Zhang neural network for approximating some expressions involving outer inversesThe representation and approximation for the weighted Moore-Penrose inverseThe representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\)On continuity of the generalized inverse \(A^{(2)}_{T,S}\)The representation and approximation for the weighted Moore-Penrose inverse in Hilbert space.Rank equalities related to a class of outer generalized inverseThe outer inverse f(2)T,S of a homomorphism of right R-modulesCramer's rules for various solutions to some restricted quaternionic linear systemsThe generalized inverse \(A_{T,*}^{(2)}\) and its applicationsIntegral and limit representations of the outer inverse in Banach space



Cites Work


This page was built for publication: A characterization and representation of the generalized inverse \(A_{T,S}^{(2)}\) and its applications