Technical Report 1999-001

Perturbation Results for Singular Values

Torsten Söderström

April 1999

The singular values of a perturbed complex-valued matrix A+epsilon B + O(epsilon2) are shown to have singular values of the form sigmai(epsilon)=sigmai + kiepsilon + O(epsilon2). Explicit expressions for the ki coefficients are derived. The cases of zero singular values as well as multiple singular values are included in the analysis.

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