How to Use np.linalg.norm in NumPy for Vector and Matrix Norms

Use np.linalg.norm to calculate the length (norm) of vectors or matrices in NumPy. You can specify the type of norm with the ord parameter, such as Euclidean norm (default) or other norms like L1 or infinity norm.

Syntax

The basic syntax of np.linalg.norm is:

• np.linalg.norm(x, ord=None, axis=None, keepdims=False)

Where:

• x: Input array (vector or matrix).
• ord: Order of the norm (default is 2 for Euclidean norm for vectors, Frobenius norm for matrices).
• axis: Axis or axes along which to compute the norm.
• keepdims: Whether to keep the dimensions of the result.

python

np.linalg.norm(x, ord=None, axis=None, keepdims=False)

Example

This example shows how to calculate the Euclidean norm of a vector and the Frobenius norm of a matrix using np.linalg.norm.

python

import numpy as np

# Vector example
vector = np.array([3, 4])
vector_norm = np.linalg.norm(vector)  # Default ord=2 (Euclidean norm)

# Matrix example
matrix = np.array([[1, 2], [3, 4]])
matrix_norm = np.linalg.norm(matrix)  # Frobenius norm by default

print(f"Vector norm (Euclidean): {vector_norm}")
print(f"Matrix norm (Frobenius): {matrix_norm}")

Output

Vector norm (Euclidean): 5.0
Matrix norm (Frobenius): 5.477225575051661

Common Pitfalls

Common mistakes when using np.linalg.norm include:

• Not specifying ord when a different norm is needed (default is Euclidean norm for vectors).
• Confusing vector norms with matrix norms; the default for matrices is the Frobenius norm.
• Not using the axis parameter correctly when working with multi-dimensional arrays.

Example of a wrong and right way to calculate the L1 norm of each row in a matrix:

python

import numpy as np

matrix = np.array([[1, -2, 3], [-4, 5, -6]])

# Wrong: forgetting axis, returns a single norm for whole matrix
wrong_norm = np.linalg.norm(matrix, ord=1)

# Right: specify axis=1 to get L1 norm of each row
right_norm = np.linalg.norm(matrix, ord=1, axis=1)

print(f"Wrong L1 norm (whole matrix): {wrong_norm}")
print(f"Right L1 norm (each row): {right_norm}")

Output

Wrong L1 norm (whole matrix): 15.0
Right L1 norm (each row): [6. 15.]

Quick Reference

Summary of common ord values for np.linalg.norm:

ord value	Norm type	Description
None or 2	Euclidean norm	Default for vectors; Frobenius norm for matrices
1	L1 norm	Sum of absolute values
np.inf	Infinity norm	Maximum absolute value
-np.inf	Negative infinity norm	Minimum absolute value
'fro'	Frobenius norm	Square root of sum of squares for matrices

Key Takeaways

Use np.linalg.norm to calculate vector or matrix norms easily in NumPy.

The default norm is Euclidean (L2) for vectors and Frobenius for matrices.

Specify the ord parameter to calculate different types of norms like L1 or infinity norm.

Use the axis parameter to compute norms along specific dimensions in arrays.

Common mistakes include forgetting axis or using the wrong ord value for your data.