title: Condition number of a matrix using numpy
body: <p>[python 2.7 and numpy v1.11.1]  I am looking at matrix condition numbers and am trying to compute the condition number for a matrix without using the function <code>np.linalg.cond()</code>.</p>
  
  <p>Based on numpy's documentation, the definition of a matrix's condition number is, "the norm of x times the norm of the inverse of x."  </p>
  
  <p>||X|| * ||X^-1||</p>
  
  <p>for the matrix </p>
  
  <pre><code>a = np.matrix([[1, 1, 1],
                 [2, 2, 1],
                 [3, 3, 0]])
  
  print np.linalg.cond(a)
  </code></pre>
  
  <p>1.84814479698e+16</p>
  
  <pre><code>print np.linalg.norm(a) * np.linalg.norm(np.linalg.inv(a))
  </code></pre>
  
  <p>2.027453660713377e+17</p>
  
  <p>Where is the mistake in my computation?</p>
  
  <p>Thanks!</p>