title: How to solve for eigen value of a matrix numerically
body: <p>I have a 3x3 matrix; I am interested in finding the eigen values and corresponding eigen vector numerically. I know for smaller system we can take determinant and will solve the determinant equation , which results in eigen values. But I have the matrix size which is pretty big; say 1000x1000. To show the problem, I have chosen 3x3 (which is dummy representation of  the actual problem). Now how to compute the eigen values and eigen vectors in python.</p>
  <pre><code>import numpy as np
  eg_matrix=np.array([[-2-x, -4, 2], [-2, 1-x, 2],[4,2,5-x]])
  </code></pre>
  <p>The system which is similar to my problem is; lambda_3 corresponds to eigen value.
  <a href="https://i.stack.imgur.com/8JM4W.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8JM4W.png" alt="dynamics stiffness matrix" /></a></p>