title: How to obtain right eigenvectors of matrix in R?
body: <p><strong><em>Edition :</em></strong> the problem in my question was I've tried to find matrix <code>S</code> from <a href="http://www.quarchome.org/correlationmatrix.pdf" rel="nofollow">equation 8</a> but this equation have error.</p>
  
  <p>How to directly obtain right eigenvectors of matrix in R ? 'eigen()' gives only left eigenvectors</p>
  
  <p><strong>Really last edition</strong>, I've made big mess here, but this question is really important for me :</p>
  
  <p><code>eigen()</code> provides some <strong>matrix</strong> of eigenvectors, from function help :</p>
  
  <p>" If ‘r &lt;- eigen(A)’, and ‘V &lt;- r$vectors; lam &lt;- r$values’, then</p>
  
  <pre><code>                      A = V Lmbd V^(-1)                         
  </code></pre>
  
  <p>(up to numerical fuzz), where <code>Lmbd =diag(lam)</code>"</p>
  
  <p>that is <code>A V = V Lmbd</code>, where V is <strong>matrix</strong> now we check it :</p>
  
  <pre><code>set.seed(1)
  A&lt;-matrix(rnorm(16),4,4)
  Lmbd=diag(eigen(A)$values)
  V=eigen(A)$vectors
  A%*%V
  
  &gt; A%*%V
                        [,1]                  [,2]          [,3]           [,4]
  [1,]  0.0479968+0.5065111i  0.0479968-0.5065111i  0.2000725+0i  0.30290103+0i
  [2,] -0.2150354+1.1746298i -0.2150354-1.1746298i -0.4751152+0i -0.76691563+0i
  [3,] -0.2536875-0.2877404i -0.2536875+0.2877404i  1.3564475+0i  0.27756026+0i
  [4,]  0.9537141-0.0371259i  0.9537141+0.0371259i  0.3245555+0i -0.03050335+0i
  &gt; V%*%Lmbd
                        [,1]                  [,2]          [,3]           [,4]
  [1,]  0.0479968+0.5065111i  0.0479968-0.5065111i  0.2000725+0i  0.30290103+0i
  [2,] -0.2150354+1.1746298i -0.2150354-1.1746298i -0.4751152+0i -0.76691563+0i
  [3,] -0.2536875-0.2877404i -0.2536875+0.2877404i  1.3564475+0i  0.27756026+0i
  [4,]  0.9537141-0.0371259i  0.9537141+0.0371259i  0.3245555+0i -0.03050335+0i
  </code></pre>
  
  <p>and I would like to find matrix of right eigenvectors <code>R</code>,<br>
  equation which define matrix of left eigenvectors <code>L</code> is :     </p>
  
  <blockquote>
  <pre><code>L A  = LambdaM L
  </code></pre>
  </blockquote>
  
  <p>equation which define matrix of right eigenvectors <code>R</code> is :  </p>
  
  <blockquote>
  <pre><code>A R = LambdaM R
  </code></pre>
  </blockquote>
  
  <p>and eigen() provides only matrix <code>V</code>:</p>
  
  <blockquote>
  <pre><code>A V = V Lmbd
  </code></pre>
  </blockquote>
  
  <p>I would like to obtain matrix <code>R</code> and <code>LambdaM</code> for real matrix <code>A</code> which may be negative-definite.</p>