Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Relative Perturbation Theory: (II) Eigenspace Variations

Ren-Cang Li

EECS Department
University of California, Berkeley
Technical Report No. UCB/CSD-94-856
December 1994

http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/CSD-94-856.pdf

In this paper, we consider how eigenspaces of a Hermitian matrix A change when it is perturbed to ~ A = D * AD and how singular values of a (nonsquare) matrix B change when it is perturbed to ~ B = D1 BD2, where D, D1 and D2 are assumed to be close to identity matrices of suitable dimensions, or either D1 or D2 close to some unitary matrix. We have been able to generalize well-known Davis-Kahan sin theta theorems. As applications, we obtained bounds for perturbations of graded matrices.


BibTeX citation:

@techreport{Li:CSD-94-856,
    Author = {Li, Ren-Cang},
    Title = {Relative Perturbation Theory: (II) Eigenspace Variations},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1994},
    Month = {Dec},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5482.html},
    Number = {UCB/CSD-94-856},
    Abstract = {In this paper, we consider how eigenspaces of a Hermitian matrix <i>A</i> change when it is perturbed to ~<i>A</i> = <i>D</i> * <i>AD</i> and how singular values of a (nonsquare) matrix <i>B</i> change when it is perturbed to ~<i>B</i> = <i>D</i>1<i>BD</i>2, where <i>D</i>, <i>D</i>1 and <i>D</i>2 are assumed to be close to identity matrices of suitable dimensions, or either <i>D</i>1 or <i>D</i>2 close to some unitary matrix. We have been able to generalize well-known Davis-Kahan sin theta theorems. As applications, we obtained bounds for perturbations of graded matrices.}
}

EndNote citation:

%0 Report
%A Li, Ren-Cang
%T Relative Perturbation Theory: (II) Eigenspace Variations
%I EECS Department, University of California, Berkeley
%D 1994
%@ UCB/CSD-94-856
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1994/5482.html
%F Li:CSD-94-856