How to find Eigenspace of a matrix using python

Question

I have a matrix which is I found its Eigenvalues and EigenVectors, but now I want to solve for eigenspace, which is Find a basis for each of the corresponding eigenspaces! and don't know how to start! by finding the null space from scipy or solve for reef(), I tried but didn't work! please help!

this is the code I am using

# import packages
import numpy as np
from numpy import linalg as LA
from scipy.linalg import null_space

# define matrix and vector
M = np.array([[0.82, 0.1],[0.18,0.9]])
v0 = np.array([[15000],[800]])

eigenVal, eigenVec = LA.eig(M)
print(eigenVal)
# Based on  the Characteristic polynomial formula 
#pol_formula =(A- \lambda I)\mathbf{v} = 0\)

identity = np.identity(2, dtype=float)
lamdbdaI= eigenVal*identity
 ## Apply the Characteristic polynomial  formula  using ###M matrix 
char_poly = M-lamdbdaI
print(char_poly)

Here I am stuck !

Answer 1

The np.linalg.eig functions already returns the eigenvectors, which are exactly the basis vectors for your eigenspaces. More precisely:

v1 = eigenVec[:,0]
v2 = eigenVec[:,1]

span the corresponding eigenspaces for eigenvalues lambda1 = eigenVal[0] and lambda2 = eigenvVal[1] .