Explicit representations of the Drazin inverse of block matrix and modified matrix

DOI10.1080/03081080701772830zbMath1176.15006OpenAlexW2172270070MaRDI QIDQ3633146

Jian-Biao Chen, Dragana S. Cvetković-Ilić, Zhaoliang Xu

Publication date: 17 June 2009

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

Full work available at URL: https://doi.org/10.1080/03081080701772830

zbMATH Keywords

Drazin inverseindexblock matrixHartwig-Meyer-Rose formula

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Matrix equations and identities (15A24)

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Characterizations and representations of the Drazin inverse involving idempotents, New representations of the group inverse of \(2 \times 2\) block matrices, The Drazin inverse of the sum of two matrices and its applications, Some results on the \((2, 2, 0)\) Drazin inverse problem, 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, Further results on the group inverses and Drazin inverses of anti-triangular block matrices, Some results on the generalized Drazin inverse of operator matrices, Additive results for the Drazin inverse of block matrices and applications, A representation for the Drazin inverse of block matrices with a singular generalized Schur complement, Generalized Drazin inverses of anti-triangular block matrices, Group inverse for block matrix with \(t\)-potent subblock, Group inverse for two classes of \(2\times 2\) anti-triangular block matrices over right Ore domains, Representations of generalized inverses and Drazin inverse of partitioned matrix with Banachiewicz-Schur forms, Representations of the Drazin inverse on solution of a class singular differential equations, Expression of the Drazin and MP-inverse of partitioned matrix and quotient identity of generalized Schur complement, The existence and representation of the Drazin inverse of a 2 × 2 block matrix over a ring, Some results on the Drazin inverse of anti-triangular matrices

Cites Work

• A note on the representations for the Drazin inverse of \(2 \times 2\) block matrices
• The perturbation theory for the Drazin inverse and its applications
• Additive perturbation results for the Drazin inverse
• An expression of the Drazin inverse of a perturbed matrix
• The Drazin inverse of a modified matrix
• Formulas for the Drazin inverse of special block matrices
• On the Generalized Drazin Inverse and Generalized Resolvent
• 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 Consistency: A Concept for the Solution of Singular Systems of Linear Equations
• Convexity and Elasticity of the Growth Rate in Size-Classified Population Models
• A Characterization and Representation of the Drazin Inverse
• Expressions for the drazin inverse of a 2×2 Block Matrix
• Representations for the Drazin Inverse of a 2 x 2 Block Matrix
• Some additive results on Drazin inverse