How to Find Eigenvalues Using NumPy in Python

Use numpy.linalg.eig to find eigenvalues of a square matrix in NumPy. It returns a tuple where the first element contains the eigenvalues as a 1D array.

Syntax

The function to find eigenvalues in NumPy is numpy.linalg.eig. It takes a square matrix as input and returns two arrays: the first contains eigenvalues, and the second contains eigenvectors.

• numpy.linalg.eig(a): a is a square 2D array (matrix).
• Returns: (w, v) where w is eigenvalues array, v is eigenvectors matrix.

python

import numpy as np

w, v = np.linalg.eig(a)

Example

This example shows how to find eigenvalues of a 2x2 matrix using numpy.linalg.eig. It prints the eigenvalues and eigenvectors.

python

import numpy as np

# Define a 2x2 matrix
matrix = np.array([[4, 2],
                   [1, 3]])

# Calculate eigenvalues and eigenvectors
eigenvalues, eigenvectors = np.linalg.eig(matrix)

print("Eigenvalues:", eigenvalues)
print("Eigenvectors:\n", eigenvectors)

Output

Eigenvalues: [5. 2.]
Eigenvectors:
 [[ 0.89442719 -0.70710678]
 [ 0.4472136   0.70710678]]

Common Pitfalls

Common mistakes when finding eigenvalues with NumPy include:

• Passing a non-square matrix, which causes an error.
• Confusing eigenvalues with eigenvectors; eigenvalues are returned as a 1D array, eigenvectors as columns of a 2D array.
• Not handling complex eigenvalues that can appear for some matrices.

Example of wrong input and correct usage:

python

import numpy as np

# Wrong: Non-square matrix
try:
    np.linalg.eig(np.array([[1, 2, 3], [4, 5, 6]]))
except np.linalg.LinAlgError as e:
    print("Error:", e)

# Right: Square matrix
matrix = np.array([[1, 2], [3, 4]])
eigenvalues, _ = np.linalg.eig(matrix)
print("Eigenvalues:", eigenvalues)

Output

Error: Last 2 dimensions of the array must be square
Eigenvalues: [-0.37228132  5.37228132]

Quick Reference

Function	Description
numpy.linalg.eig(a)	Returns eigenvalues and eigenvectors of square matrix a
a	Square 2D NumPy array (matrix)
Returns	Tuple (eigenvalues array, eigenvectors matrix)
Eigenvalues	1D array of eigenvalues
Eigenvectors	2D array with eigenvectors as columns

Key Takeaways

Use numpy.linalg.eig to find eigenvalues and eigenvectors of a square matrix.

Input matrix must be square; otherwise, NumPy raises an error.

Eigenvalues are returned as a 1D array; eigenvectors are columns in a 2D array.

Some matrices may have complex eigenvalues; handle them accordingly.

Always check matrix shape before calling the function to avoid errors.