On the invariance of perturbed null vectors under column scaling

Summary It is shown that the approximate null vector of a perturbed degenerate matrix behaves linearly under column scaling up to second order terms in the perturbation. This result has important consequences for an estimation technique known to numerical analysts as total least squares and to statisticians as latent root regression.Dedicated to F.L. Bauer on the occasion of his 60th birthdayDepartment of Computer Science and Institute for Physical Science and Technology, University of Maryland at College Park. This work was done while the author was at the Scientific Computing Division of the National Bureau of Standards