Ren-Cang Li

EECS Department, University of California, Berkeley

Technical Report No. UCB/CSD-94-856

, 1994

http://www2.eecs.berkeley.edu/Pubs/TechRpts/1994/CSD-94-856.pdf

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.

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BibTeX citation:

@techreport{Li:CSD-94-856,
    Author= {Li, Ren-Cang},
    Title= {Relative Perturbation Theory: (II) Eigenspace Variations},
    Year= {1994},
    Month= {Dec},
    Url= {http://www2.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://www2.eecs.berkeley.edu/Pubs/TechRpts/1994/5482.html
%F Li:CSD-94-856