import numpy

A = numpy.array([[1, 2], [2, 1]])

u, P = numpy.linalg.eig(A)

D = numpy.diag(u)

print("P: \n", P)
print("D: \n", D)
print("Inverse of P: \n", numpy.linalg.inv(P))

A_cal = P.dot(D).dot(numpy.linalg.inv(P))
if numpy.allclose(A, A_cal):
    print("A is eigen decomposed")
else:
    print("A cannot be eigen decomposed")

Here, A is a square matrix. We are using the numpy.linalg.eig() function to calculate the eigen values and eigen vectors of A. Here, u contains the eigenvalues, and P is a matrix whose columns are the eigenvectors of A.

So, we can get the diagonal matrix D from the eigenvalue u using the numpy.diag() function. And we get the inverse of P using the numpy.linalg.inv() function.

The output of the mentioned program will be:

P: 
 [[ 0.70710678 -0.70710678]
 [ 0.70710678  0.70710678]]
D: 
 [[ 3.  0.]
 [ 0. -1.]]
Inverse of P: 
 [[ 0.70710678  0.70710678]
 [-0.70710678  0.70710678]]
A is eigen decomposed