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We study the denoising of low-rank matrices by singular value shrinkage.Recent work of Gavish and Donoho constructs a framework for finding optimalsingular value shrinkers for a wide class of loss functions. We use thisframework to derive the optimal shrinker for operator norm loss. The optimalshrinker matches the shrinker proposed by Gavish and Donoho in the special caseof square matrices, but differs for all other aspect ratios. We preciselyquantify the gain in accuracy from using the optimal shrinker. We also showthat the optimal shrinker converges to the best linear predictor in theclassical regime of aspect ratio zero.

Optimal singular value shrinkage for operator norm loss