In the proof of Lemma 10, the first inequality in the bound on \| \hat{B}_x - \tilde{B}_x \|_2 should be changed to \| \hat{B}_x - \tilde{B}_x \|_2 = \| (\hat{U}^\top P_{3,x,1}) (\hat{U}^\top P_{2,1})^+ - (\hat{U}^\top \hat{P}_{3,x,1}) (\hat{U}^\top \hat{P}_{2,1})^+ \|_2 \leq \| (\hat{U}^\top P_{3,x,1}) ((\hat{U}^\top P_{2,1})^+ - (\hat{U}^\top \hat{P}_{2,1})^+) \|_2 + \| \hat{U}^\top (P_{3,x,1} - \hat{P}_{3,x,1}) (\hat{U}^\top \hat{P}_{2,1})^+ \|_2 (i.e., P_{2,1} is replaced by \hat{P}_{2,1} at the very end). Thanks to Michael Collins for pointing this out. (Miraculously, the bounds on Delta_x and Delta in the lemma statement remain true.) DH 2012-11-25