How to compute the eigenvalues and right eigenvectors of a given square array using NumPY?

In this article, we will discuss how to compute the eigenvalues and right eigenvectors of a given square array using NumPy library. 

Example:

Suppose we have a matrix as: 
[[1,2],
[2,3]] 

Eigenvalue we get from this matrix or square array is: 
[-0.23606798 4.23606798]

Eigenvectors of this matrix are: 
[[-0.85065081 -0.52573111], 
[ 0.52573111 -0.85065081]] 

To know how they are calculated mathematically see this Calculation of EigenValues and EigenVectors. In the below examples, we have used numpy.linalg.eig() to find eigenvalues and eigenvectors for the given square array. 

Syntax: numpy.linalg.eig()

Parameter: An square array.

Return: It will return two values first is eigenvalues and second is eigenvectors.

Example 1:

# importing numpy library
import numpy as np

# create numpy 2d-array
m = np.array([[1, 2],
              [2, 3]])

print("Printing the Original square array:\n",
      m)

# finding eigenvalues and eigenvectors
w, v = np.linalg.eig(m)

# printing eigen values
print("Printing the Eigen values of the given square array:\n",
      w)

# printing eigen vectors
print("Printing Right eigenvectors of the given square array:\n"
      v)

Output:

Printing the Original square array:
 [[1 2]
 [2 3]]
Printing the Eigen values of the given square array:
 [-0.23606798  4.23606798]
Printing Right eigenvectors of the given square array:
 [[-0.85065081 -0.52573111]
 [ 0.52573111 -0.85065081]]

Example 2:

# importing numpy library
import numpy as np

# create numpy 2d-array
m = np.array([[1, 2, 3],
              [2, 3, 4],
              [4, 5, 6]])

print("Printing the Original square array:\n",
      m)

# finding eigenvalues and eigenvectors
w, v = np.linalg.eig(m)

# printing eigen values
print("Printing the Eigen values of the given square array:\n",
      w)

# printing eigen vectors
print("Printing Right eigenvectors of the given square array:\n",
      v)

Output:

Printing the Original square array:
 [[1 2 3]
 [2 3 4]
 [4 5 6]]
Printing the Eigen values of the given square array:
 [ 1.08309519e+01 -8.30951895e-01  1.01486082e-16]
Printing Right eigenvectors of the given square array:
 [[ 0.34416959  0.72770285  0.40824829]
 [ 0.49532111  0.27580256 -0.81649658]
 [ 0.79762415 -0.62799801  0.40824829]]