Some additive results on Drazin inverse

By R. Hartwig, Guo-rong Wang, Yimin Wei. 2001

192 citations recorded by the source corpus.

Some additive perturbation results for Drazin inverses are given. In particular, a formula is given for the Drazin inverse of a sum of two matrices, when one of the products of these matrices vanishes. Some special applications of this are also considered.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/f17619d42638a1186ba7d083622585984bf3ecc3

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Numerical Analysis

Citations in the corpus

Additive results for the generalized Drazin inverse (2002, unknown): “Hartwig, Wang and Wei investigated this problem in a finite dimensional case (see [13]).”
On the Drazin inverse of the sum of two operators and its application to operator matrices (2009, methodology): “322 (2001) 207–217] for matrices and by Djordjević and Wei [D.S. Djordjević, Y. Wei, Additive results for the generalized Drazin inverse, J. Aust.”
New additive results for the generalized Drazin inverse (2010, background): “Some additive properties and the explicit expressions for the GD-inverse of the sum are obtained in [4,8,11,15,21,37].”
A note on the Drazin inverse of an anti-triangular matrix (2009, methodology): “20 The Drazin inverse of an operator or a matrix has various applications in singular differential 21 equations and singular difference equations, Markov chains, and iterative methods (see [2–5,6,8,9,15, 22 16,18,20,30,31,32] ).”
The Drazin inverses of sum and difference of idempotents (2009, methodology): “In recent years, the characterizations of the Drazin inverses of matrices or operators on a Hilbert space have been considered bymany authors (see [1,3,7–14,16–20]).”
A note on the representation for the Drazin inverse of 2×2 block matrices (2008, background): “The Drazin inverse of a square matrix has various applications in singular differential equations and singular difference equations, Markov chains and iterative methods (see [2,4,8,10,14,19]).”