Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

Konstantin E. Avrachenkov; Moshe Haviv

doi:10.1016/S0024-3795(02)00729-2

Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

Konstantin E. Avrachenkov^*, Moshe Haviv

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Linear Algebra and Its Applications
Volume	369
Issue number	SUPP.
DOIs	https://doi.org/10.1016/S0024-3795(02)00729-2
State	Published - 1 Aug 2003

Keywords

Analytic perturbation
Eigenvalue problem
Group inverse
Null space
Reduction technique
Singularity

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10.1016/S0024-3795(02)00729-2

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abstract = "We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices.",

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AB - We consider properties of a null space of an analytically perturbed matrix. In particular, we obtain Taylor expansions for the eigenvectors which constitute a basis for the perturbed null space. Furthermore, we apply these results to the calculation of Puiseux expansion of the perturbed eigenvectors in the case of general eigenvalue problem as well as to the calculation of Laurent series expansions for the perturbed group inverse and pseudoinverse matrices.

KW - Analytic perturbation

KW - Eigenvalue problem

KW - Group inverse

KW - Null space

KW - Reduction technique

KW - Singularity

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Perturbation of null spaces with application to the eigenvalue problem and generalized inverses

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Keywords

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