This may be trivial but I couldn't figure it out. If SVD of matrix $X$ is $X = U \Sigma V^*$. For a constant value $c$ what is the SVD of $X-c$ ? From experiments it looks like only the largest singular value is affected.
2026-03-26 04:32:54.1774499574
Singular value decomposition of matrix shifted by a constant
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This problem is addressed in Shifted Randomized SVD algorithm. An implementation is available here.