The Probability of a Subspace Swap in the SVD

In this paper we extend the work of Tufts, Kot, and Vaccaro (TKV) to improve the analytical characterization of threshold breakdown in SVD methods. Our results sharpen the TKV results by lower bounding the probability of a subspace swap in the SVD. Our key theoretical result is the characteristic function for a random variable whose probability of exceeding zero bounds the probability of a threshold breakdown.