5. Perturbation Theorems for Singular Values
Society for Industrial and Applied Mathematics eBooks · 1995
The singular values of a matrix are very stable with respect to changes in the elements of the matrix. Perturbations of the elements of a matrix produce perturbations of the same, or smaller, magnitude in the singular values. The purpose of this chapter is to present Theorems (5.7) and (5.10), which provide precise statements about this stability, and Theorem (5.12), which gives bounds on the perturbation of singular values due to removing a column, or row, of a matrix.