title: how to project a low pca dimension point back to original pca space in matlab
body: <p>I have a 455 samples by 30 features matrix <code>X</code>. I am using the following pca projection into 2D:</p>
  
  <pre><code>[coeff, score, ~, ~, ~, mu]=pca(X');
  gscatter(score(:,1),score(:,2),Y,'br','.');
  </code></pre>
  
  <p>Where <code>Y</code> are lables of the 455 samples. </p>
  
  <p>Assuming I have a set of new 2D points <code>z</code> n samples by 2, which I want to project back to the 30d dimention, can I use <code>coeff</code> to project it? Is the following valid:</p>
  
  <pre><code>projecte30dz=z*coeff(1:2,:);
  </code></pre>
  
  <p>How do I project a new point in the low pca dimension back to the original space?</p>