Perturbation bounds in connection with singular value decomposition
- Cite this article as:
- Wedin, PÅ. BIT (1972) 12: 99. doi:10.1007/BF01932678
LetA be anm ×n-matrix which is slightly perturbed. In this paper we will derive an estimate of how much the invariant subspaces ofAHA andAAH will then be affected. These bounds have the sin ϑ theorem for Hermitian linear operators in Davis and Kahan  as a special case. They are applicable to computational solution of overdetermined systems of linear equations and especially cover the rank deficient case when the matrix is replaced by one of lower rank.