Before revision:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and the stability of the singular value thresholding operator ) can be solved with the help of these new results .
After revision:  Following this, we proceed to show that two other popular stability problems (i.e., the stability of the Principal Component Analysis and an error bound on the singular value thresholding operator ) can be solved with the help of these new results .