title: Eigen vector in SVD
body: <p>Im going to compute the eigen value and eigen vector from my Matrix data fro the classification. </p>
  
  <p>The rows represent the different classes and the columns represent the features.</p>
  
  <p>So, for example if I have </p>
  
  <pre><code> X= 
    [2 3 4]  
    [3 2 4]   
    [4 5 6]  
    [8 9 0]
  </code></pre>
  
  <p><strong>I have to use SVD instead of PCA because the matrix is not square.</strong></p>
  
  <p>What I have done are:</p>
  
  <ol>
  <li><p>Compute the mean for each row. So I have</p>
  
  <pre><code>Mean=  
    M1  
    M2  
    M3  
    M4
  </code></pre></li>
  <li><p>Substract my matrix <strong>X</strong> with the Mean</p>
  
  <pre><code> Substract= 
  
  [2-M1 3-M1 4-M1]  
  [3-M2 2-M2 4-M2]   
  [4-M3 5-M3 6-M3]  
  [8-M4 9-M4 0-M4]
  </code></pre></li>
  <li><p>Covariance Matrix = (Substract*Substract^t)/(4-1)</p></li>
  <li><p>[U,S,V] = svd(X)</p></li>
  </ol>
  
  <p>Are all my step right? By compute the mean for each row (as the classes)?   </p>
  
  <p>If I want to project my data into eigen space (for dimensionality reduction), which is the eigen vector (U or V)?? </p>