Result: Perturbation of null spaces with application to the eigenvalue problem and generalized inverses
Title:
Perturbation of null spaces with application to the eigenvalue problem and generalized inverses
Authors:
Source:
Linear Algebra and its Applications. 369:1-25
Publisher Information:
Elsevier BV, 2003.
Publication Year:
2003
Subject Terms:
Numerical computation of eigenvalues and eigenvectors of matrices, numerical examples, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, null space, Algebra and Number Theory, Singularity, reduction technique, eigenvectors, Reduction technique, Inequalities involving eigenvalues and eigenvectors, singularity, 01 natural sciences, Null space, pseudoinverse, group inverse, Eigenvalue problem, Group inverse, analytic perturbation, Analytic perturbation, eigenvalue problem, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Geometry and Topology, 0101 mathematics
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0024-3795
DOI:
10.1016/s0024-3795(02)00729-2
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....8b2df8d4bca25b4a2236a7d0c38ed43f
Database:
OpenAIRE
Further Information
This paper concerns \[ A(\varepsilon) x(\varepsilon)= \lambda(\varepsilon) x(\varepsilon)\tag{1} \] and in particular \[ A(\varepsilon)= \sum^\infty_{k=0} \varepsilon^k A_k,\quad A_k\in\mathbb{R}^{n\times n},\tag{2} \] where (2) converges for \(|\varepsilon|\leq R\), \(R> 0\), and gives Taylor series for the eigenvectors that constitute a basis for the perturbed null space. This is applied to the calculation of Laurent series for the perturbed group inverse and pseudoinverse matrices. A few formal and one numerical examples are included.