Representations for the Drazin inverse of the sum \(P+Q+R+S\) and its applications

DOI10.1016/j.laa.2008.08.007zbMath1190.15004OpenAlexW2029416879MaRDI QIDQ958035

Zhaoliang Xu, Yi-Min Wei, Jian-Biao Chen

Publication date: 2 December 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.08.007

zbMATH Keywords

Drazin inverseindexgroup inversepseudo-block decomposition

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09)

Related Items (14)

Characterizations and representations of the Drazin inverse involving idempotents ⋮ Expressions for the \(g\)-Drazin inverse of additive perturbed elements in a Banach algebra ⋮ New representations of the group inverse of \(2 \times 2\) block matrices ⋮ On deriving the Drazin inverse of a modified matrix ⋮ Representation of the Drazin inverse for special block matrix ⋮ Representations for the Drazin inverse of \(2\times 2\) block-operator matrix with singular Schur complement ⋮ Perturbation bound of the group inverse and the generalized Schur complement in Banach algebra ⋮ Some results on the generalized Drazin inverse of operator matrices ⋮ A representation for the Drazin inverse of block matrices with a singular generalized Schur complement ⋮ Group inverse for block matrix with \(t\)-potent subblock ⋮ The Drazin inverse of the sum of four matrices and its applications ⋮ Representations of the Drazin inverse on solution of a class singular differential equations ⋮ A note on additive results for the Drazin inverse ⋮ Strongly Drazin inverse in rings

Cites Work

• Unnamed Item
• Unnamed Item
• Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices -- application of perturbation theory for simple invariant subspaces
• A note on the representations for the Drazin inverse of \(2 \times 2\) block matrices
• A note on the representation for the Drazin inverse of \(2 \times 2\) block matrices
• Quotient convergence and multi-splitting methods for solving singular linear equations
• Convergence and quotient convergence of iterative methods for solving singular linear equations with index one
• On the solution of singular linear systems of algebraic equations by semiiterative methods
• Nonnegative group inverses
• The perturbation theory for the Drazin inverse and its applications
• On group inverse of singular Toeplitz matrices
• Additive perturbation results for the Drazin inverse
• Representations of the Drazin inverse for a class of block matrices
• The Drazin inverse of a modified matrix
• Generalized inverses. Theory and applications.
• The group inverse of a triangular matrix
• Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index
• Formulas for the Drazin inverse of special block matrices
• Splittings ofM-operators: Irreducibility and the index of the iteration operator
• On the Generalized Drazin Inverse and Generalized Resolvent
• The generalized Schur complement in group inverses and (k + 1)-potent matrices
• The Drazln inverse and systems of second order linear differential equations
• Updating finite markov chains by using techniques of group matrix inversion
• APPLICATIONS OF THE DRAZIN INVERSE TO THE HILL CRYPTOGRAPHIC SYSTEM. PART III.
• The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
• The Index and the Drazin Inverse of Block Triangular Matrices
• Iterative and Semi-Iterative Methods for Computing Stationary Probability Vectors of Markov Operators
• Iterative Consistency: A Concept for the Solution of Singular Systems of Linear Equations
• The group inverse of a companion matrix
• Convexity and Elasticity of the Growth Rate in Size-Classified Population Models
• On the Index of Block Upper Triangular Matrices
• Equivalence of conditions for convergence of iterative methods for singular equations
• Expressions for the drazin inverse of a 2×2 Block Matrix
• A Perturbation Bound of the Drazin Inverse of a Matrix by Separation of Simple Invariant Subspaces
• An improvement on perturbation bounds for the Drazin inverse
• Representations for the Drazin Inverse of a 2 x 2 Block Matrix
• Some additive results on Drazin inverse

This page was built for publication: Representations for the Drazin inverse of the sum \(P+Q+R+S\) and its applications