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On the Application of Schur Complements to the Spectral Analysis of Hermitian Matrices

Rubin, Olof LU (2019) In Master's Theses in Mathematical Sciences MATM01 20191
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Abstract (Swedish)
A second order expansion of the eigenvalues of a parameter perturbation of Hermitian matrices is derived using matrix decomposition methods. The method developed is then applied to give a novel proof of a second order approximation of the eigenvalues of a global perturbation of Hermitian matrices first described by M. Carlsson. The result generalizes an approximation given by G.W Stewart which treats the case of simple eigenvalues. This global second order approximation is then applied to the study of perturbations of singular values for matrices with non-empty kernel.
Please use this url to cite or link to this publication:
author
Rubin, Olof LU
supervisor
organization
course
MATM01 20191
year
type
H2 - Master's Degree (Two Years)
subject
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3103-2019
ISSN
1404-6342
other publication id
2019:E12
language
English
id
8973651
date added to LUP
2026-05-05 14:06:13
date last changed
2026-05-05 14:06:15
@misc{8973651,
  abstract     = {{A second order expansion of the eigenvalues of a parameter perturbation of Hermitian matrices is derived using matrix decomposition methods. The method developed is then applied to give a novel proof of a second order approximation of the eigenvalues of a global perturbation of Hermitian matrices first described by M. Carlsson. The result generalizes an approximation given by G.W Stewart which treats the case of simple eigenvalues. This global second order approximation is then applied to the study of perturbations of singular values for matrices with non-empty kernel.}},
  author       = {{Rubin, Olof}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{On the Application of Schur Complements to the Spectral Analysis of Hermitian Matrices}},
  year         = {{2019}},
}