Is there a simple transformation to apply to a matrix $A$ so that its smallest singular value becomes larger than an arbitrary value $\epsilon$, while the other singular values are perturbed as little as possible?
2026-03-27 14:10:31.1774620631
How to impose a lower bound to the smallest singular value?
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For example: $A+(\sigma_{n-1}-\sigma_n)u_nv_n^T$ will have the same SVD as $A$ except with $\sigma_{n}=\sigma_{n-1}$.