Before revision:  Moreover, since \alpha_p < \omega  for every p, our algorithm has a better dependence on n than that in the singular value decomposition for every p. Crucial to our analysis is the use of dimensionality reduction for Ky-Fan p-norms.
After revision:  Moreover, since \alpha_p < \omega - 1 for every p, our algorithm has a better dependence on n than that in the singular value decomposition for every p. Crucial to our analysis is the use of dimensionality reduction for Ky-Fan p-norms.