title: What does selecting the largest eigenvalues and eigenvectors in the covariance matrix mean in data analysis?
body: <p>Suppose there is a matrix <code>B</code>, where its size is a <code>500*1000 double</code>(Here, <code>500</code> represents the number of observations and <code>1000</code> represents the number of features).</p>
  
  <p><code>sigma</code> is the covariance matrix of <code>B</code>, and <code>D</code> is a diagonal matrix whose diagonal elements are the eigenvalues of <code>sigma</code>. Assume <code>A</code> is the eigenvectors of the covariance matrix <code>sigma</code>.</p>
  
  <p>I have the following questions:</p>
  
  <ol>
  <li><p>I need to select the first <code>k = 800</code> eigenvectors corresponding to the eigenvalues with the largest magnitude to rank the selected features. The final matrix named <code>Aq</code>. How can I do this in MATLAB?</p></li>
  <li><p>What is the meaning of these selected eigenvectors?</p></li>
  <li><p>It seems the size of the final matrix <code>Aq</code> is <code>1000*800 double</code> once I calculate <code>Aq</code>. The time points/observation information of <code>500</code> has disappeared. For the final matrix <code>Aq</code>, what does the value <code>1000</code> in matrix <code>Aq</code> represent now? Also, what does the value <code>800</code> in matrix <code>Aq</code> represent now?</p></li>
  </ol>