eig.py

# http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
#numpy.linalg.eig(a)[source]
#Compute the eigenvalues and right eigenvectors of a square array.
#
#Parameters:	
#a : (..., M, M) array
#Matrices for which the eigenvalues and right eigenvectors will be computed
#Returns:	
#w : (..., M) array
#The eigenvalues, each repeated according to its multiplicity. The eigenvalues are not necessarily ordered. The resulting array will be #always be of complex type. When a is real the resulting eigenvalues will be real (0 imaginary part) or occur in conjugate pairs
#v : (..., M, M) array
#The normalized (unit “length”) eigenvectors, such that the column v[:,i] is the eigenvector corresponding to the eigenvalue w[i].
#Raises:	
#LinAlgError :
#If the eigenvalue computation does not converge.



A = np.array(
    [[ 2, 1],
     [-0.5,-1.5]])

la, v = np.linalg.eig(A)
print "la",la
print "v",v


print v[0][1]**2 + v[1][1]**2
print v[0][1]**2 / v[1][1]**2


# eig.rb
# (This code is reference of https://gist.github.com/maehrm/43058b429cdb179671c5)
## coding: utf-8
#require 'matrix'
# 
#a = Matrix[[2, 1], [-0.5, -1.5]]
#p a.eigensystem.eigenvalues        # => [1.8507810593582121, -1.3507810593582121]
#p a.eigensystem.eigenvector_matrix # => Matrix[[0.9890493903846761, -0.31580578969441475], [-0.14758490227560742, 1.0581960585437078]]

ruby_v1 = -0.31580578969441475
ruby_v2 = 1.0581960585437078
print (ruby_v1)**2 + ruby_v2**2
print (ruby_v1)**2 / ruby_v2**2

# ---------- output -------------#
# la [ 1.85078106 -1.35078106]
# v [[ 0.98904939 -0.28597431]
#    [-0.1475849   0.95823729]]
# 1.0
# 0.089065168985
# 
# 1.21951219512
# 0.089065168985