title: calculating the eigenvector from a complex eigenvalue in opencv
body: <p>I am trying to calculate the eigenvector of a 4x4 matrix in opencv.<br>
  For this I first calculate the eigenvalue according to this formula:</p>
  
  <pre><code>Det( A - lambda * identity matrix ) = 0
  </code></pre>
  
  <p>From <a href="http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#Matrices" rel="nofollow">wiki on eigenvalues and eigenvectors</a>.<br>
  After solving this, it gives me 4 eigenvalues that look something like this:</p>
  
  <pre><code>0.37789 + 1.91687i
  0.37789 - 1.91687i
  0.412312 + 1.87453i
  0.412312 - 1.87453i
  </code></pre>
  
  <p>From these 4 eigenvalues I take the highest value and I want use that with this formula:</p>
  
  <pre><code>( A - lambda * identity matrix ) v = 0
  </code></pre>
  
  <p>I tried to use my original matrix A with the opencv function "eigen()", but this doesn't give me the results I am looking for.<br>
  I also tried to use RREF (reduced row echelon form), however I don't know how to do this with complex eigenvalues.</p>
  
  <p><strong>So my question is, how would you calculate this eigenvector?</strong></p>
  
  <p>I plugged my data in to <a href="http://www.wolframalpha.com/input/?i=solve%20eigenvector&amp;a=*C.solve%20eigenvector-_*Calculator.dflt-&amp;f2=%7B%7B0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C1.90%2C0.01%2C-0.16%7D%2C%7B-1.90%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C0.16%2C0.01%7D%2C%7B0.01%2C0.16%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C-1.90%7D%2C%7B-0.16%2C0.01%2C1.90%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%7D%7D&amp;f=Eigenvector.eigvecmatrix_%7B%7B0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C1.90%2C0.01%2C-0.16%7D%2C%7B-1.90%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C0.16%2C0.01%7D%2C%7B0.01%2C0.16%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%2C-1.90%7D%2C%7B-0.16%2C0.01%2C1.90%2C0.40%20-%20%28%200.41%20%2B%201.87i%20%29%7D%7D" rel="nofollow">wolframalpha</a> to see what my results should be.</p>