title: Matrix Low Rank Approximation using Matlab
body: <p>Consider a 256 x 256 matrix <code>A</code>. I'm familiar with how to calculate low rank approximations of <code>A</code> using the SVD.</p>
  
  <p>Typically after using <code>[U S V] = svd(A)</code>, I would use <code>Ak = U(:,1:k)*S(1:k,1:k)*V(:,1:k)';</code> to get the rank <code>k</code> approximation of <code>A</code>.</p>
  
  <p>My question is how do I create a vector <code>E</code> such that,
  <code>E(k) = norm(A-Ak)</code> for <code>k=1,2,3.....,256</code>. That is <code>E</code> is a column vector of 256 elements each of which is <code>norm(A-Ak)</code></p>