In our previous article, we discussed what eigen values and eigenvectors of a square matrix are and how we can calculate the eigenvalues and eigenvectors of a square matrix mathematically. We discussed that if A is a square matrix, then

If we solve for λ, we get the eigenvalues. And if we solve for u for a particular value of λ, we get the eigenvector for the corresponding eigenvalue.

We can use the following Python code to calculate the eigenvalues and eigenvectors of a square matrix A.

import numpy

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

w, v = numpy.linalg.eig(A)
print(w)
print(v)

Here, A is a square matrix. We are using the eig() function from the numpy.linalg module to get the eigenvalues and the corresponding eigenvectors of A. The variable w here contains the eigenvalues. And v is a matrix whose columns contain the eigenvectors.

The output of the mentioned program will be:

[ 3. -1.]
[[ 0.70710678 -0.70710678]
 [ 0.70710678  0.70710678]]