  Randomized matrix algorithms have become workhorse tools in scientific
computing and machine learning. To use these algorithms safely in applications,
they should be coupled with posterior error estimates to assess the quality of
the output. To meet this need, this paper proposes two diagnostics: a
leave-one-out error estimator for randomized low-rank approximations and a
jackknife resampling method to estimate the variance of the output of a
randomized matrix computation. Both of these diagnostics are rapid to compute
for randomized low-rank approximation algorithms such as the randomized SVD and
randomized Nystr\"om approximation, and they provide useful information that
can be used to assess the quality of the computed output and guide algorithmic
parameter choices.
