text: '''Given the matrix below, find the eigenvalues (name these variable eig1 and eig2). For each eigenvalue find its eigenvector (call these variables eigenvector1 and eigenvector2).
      1    4
      3    5
  Don't forget to create the matrix above.
  Consider the rotation matrix for two dimensions. (for example - we see that for zero degrees this matrix is just a 2-by-2 identity matrix.) Find the eigenvalues for a 45 degree rotation (call these variables eig_rot1 and eig_rot2). For each eigenvalue find its eigenvalue (call these variables eigenvector_rot1 and eigenvector_rot2).'''
  
  import math
  import numpy as np
  
  A = np.matrix([[1, 4],
                 [3, 5]])
  
  eig1, eig2 = np.linalg.eigvals(A)
  print(eig1, eig2)
  
  R = np.matrix([[math.cos(math.pi/4), -math.sin(math.pi/4)],
                 [math.sin(math.pi/4), math.cos(math.pi/4)]])
  T = A*R
  eig_rot1, eig_rot2 = np.linalg.eigvals(T)
  print(T)
  eig_rots, eigen_vectors = np.linalg.eig(T)
  print(eigen_vectors, eig_rots)
  print(eig_rot1, eig_rot2)
  