The perturbation theory for the Drazin inverse and its applications (Q1359186)
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scientific article; zbMATH DE number 1026437
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The perturbation theory for the Drazin inverse and its applications |
scientific article; zbMATH DE number 1026437 |
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The perturbation theory for the Drazin inverse and its applications (English)
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24 June 1997
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For an \(n\times n\) matrix \(A\), let \(A^D\) denote the Drazin inverse of \(A\). The main result of this paper is the following: If \(B=A+E\) where \(E=AA^DEAA^D\) and \(\delta=|A^DE|<1\), then \((|B^D- A^D|)/|A^D|\leq\delta/(1- \delta)\). An application to a perturbed linear system is given.
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perturbation theory
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Drazin inverse
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