title: R solve:system is exactly singular
body: <p>I am solving simple optimization problem. The data set has 26 columns and over 3000 rows.
  The source code looks like </p>
  
  <pre><code>Means   &lt;- colMeans(Returns)
  Sigma   &lt;- cov(Returns)
  invSigma1 &lt;- solve(Sigma)
  </code></pre>
  
  <p>And everything works perfect- but then I want to do the same for shorter period (only 261 rows) and the solve function writes the following error:</p>
  
  <pre><code>solve(Sigma)
  Error in solve.default(Sigma) : 
    Lapack routine dgesv: system is exactly singular 
  </code></pre>
  
  <p>Its weird because when I do the same with some random numbers:</p>
  
  <pre><code>Returns&lt;-matrix(runif(6786,-1,1), nrow=261)
  Means   &lt;- colMeans(Returns)
  Sigma   &lt;- cov(Returns)
  invSigma &lt;- solve(Sigma)
  </code></pre>
  
  <p>no error occurs at all. Could someone explain me where could be the problem and how to treat it.
  Thank you very much,
  Alex</p>