title: The fastest way to calculate eigenvalues of large matrices
body: <p>Until now I used numpy.linalg.eigvals to calculate the eigenvalues of quadratic matrices with at least 1000 rows/columns and, for most cases, about a fifth of its entries non-zero (I don't know if that should be considered a sparse matrix). I found another <a href="https://stackoverflow.com/questions/6684238/whats-the-fastest-way-to-find-eigenvalues-vectors-in-python">topic</a> indicating that scipy can possibly do a better job.</p>
  
  <p>However, since I have to calculate the eigenvalues for hundreds of thousands of large matrices of increasing size (possibly up to 20000 rows/columns and yes, I need ALL of their eigenvalues), this will always take awfully long. If I can speed things up, even just the tiniest bit, it would most likely be worth the effort.</p>
  
  <p>So my question is: Is there a faster way to calculate the eigenvalues when not restricting myself to python?</p>