@TechReport{	  it:1999-001,
  author	= {Torsten S{\"o}derstr{\"o}m},
  title		= {Perturbation Results for Singular Values},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Systems and Control},
  year		= {1999},
  number	= {1999-001},
  month		= apr,
  abstract	= {The singular values of a perturbed complex-valued matrix
		  $A+\epsilon B + O(\epsilon^2)$ are shown to have singular
		  values of the form $\sigma_i(\epsilon)=\sigma_i +
		  k_i\epsilon + O(\epsilon^2)$. Explicit expressions for the
		  $k_i$ coefficients are derived. The cases of zero singular
		  values as well as multiple singular values are included in
		  the analysis.}
}