, Volume 12, Issue 1, pp 99-111

Perturbation bounds in connection with singular value decomposition

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Abstract

LetA be anm ×n-matrix which is slightly perturbed. In this paper we will derive an estimate of how much the invariant subspaces ofA H A andAA H will then be affected. These bounds have the sin ϑ theorem for Hermitian linear operators in Davis and Kahan [1] 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.