Uppsala University Department of Information Technology

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 sigma_i(epsilon)=sigma_i + k_iepsilon + O(epsilon²). Explicit expressions for the k_i coefficients are derived. The cases of zero singular values as well as multiple singular values are included in the analysis.

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