Finite algorithms for the (2)-generalized inverse

DOI10.1080/03081089508818420zbMath0855.65034OpenAlexW2018142726MaRDI QIDQ4871381

Yong-Lin Chen

Publication date: 11 February 1997

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

Full work available at URL: https://doi.org/10.1080/03081089508818420

zbMATH Keywords

finite algorithm(2)-generalized inverse

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09)

Related Items (22)

Representation and approximate for generalized inverse \(A_{T,S}^{(2)}\): revisited ⋮ An efficient method for computing the outer inverse \(A_{T,S}^{(2)}\) through Gauss-Jordan elimination ⋮ Condensed Cramer rule for some restricted quaternion linear equations ⋮ A note on the representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\) ⋮ Determinantal representation of the generalized inverses over the quaternion skew field with applications ⋮ Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\) ⋮ PCR algorithm for parallel computing the solution of the general restricted linear equations ⋮ Properties and computation of continuous-time solutions to linear systems ⋮ New results on condensed Cramer's rule for the general solution to some restricted quaternion matrix equations ⋮ (T,S) splitting methods for computing the generalized inverse and rectangular systems^∗ ⋮ Operator and matrix representation for the generalized inverse \(A_{T,S}^{(2)}\) ⋮ An efficient method to compute different types of generalized inverses based on linear transformation ⋮ Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field ⋮ Bott-Duffin inverse over the quaternion skew field with applications ⋮ Unnamed Item ⋮ Determinantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applications ⋮ DFT calculation for the \(\{2\}\)-inverse of a polynomial matrix with prescribed image and kernel ⋮ Limit representations of generalized inverses and related methods ⋮ Cramer's rule for a system of quaternion matrix equations with applications ⋮ Representation and approximation for the Drazin inverse \(A^{(\text{d})}\) ⋮ The representation and approximation for the generalized inverse \(A^{(2)}_{T,S}\) ⋮ Cramer's rules for various solutions to some restricted quaternionic linear systems

Cites Work

• Unnamed Item
• A new proof for Decell's finite algorithm for generalized inverses
• On g-inverses and the nonsingularity of a bordered matrix \(\begin{pmatrix} A&B\\ C&0\end{pmatrix}\)
• The generalized Bott-Duffin inverse and its applications
• A finite algorithm for computing the weighted Moore-Penrose inverse \(A^ +_{MN}\)
• A Drazin inverse for rectangular matrices
• A modified Leverrier-Faddeev algorithm for matrices with multiple eigenvalues
• The Souriau-Frame algorithm and the Drazin pseudoinverse
• More on the Souriau–Frame Algorithm and the Drazin Inverse
• Representations and cramer rules for the solution of a restricted Matrix Equation^∗
• A cramer rule for solution of the general restricted linear equation^∗
• An Application of the Cayley-Hamilton Theorem to Generalized Matrix Inversion

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