What is the L² norm of a vector?

The norm of a vector v is mathematically defined as follows:

When q=1, the vector norm is called the L¹ norm or the Manhattan norm. So, the L¹ norm of a vector is mathematically defined as follows:

And when q=2, the vector norm is called the L² norm. So, the L² norm of a vector is mathematically defined as follows:

This L² norm of a vector is also called the Euclidian norm. Let’s look at an example. Let’s say v is a vector that has the following components:

So, the L² norm of the vector v is given by:

How to calculate the L² norm of a vector using Python?

We can use the following Python code to calculate the L2 norm of a vector using NumPy.

import numpy
from numpy.linalg import norm

v = numpy.array([1, 2, -3])
l2 = norm(v)

print("Vector v: \n", v)
print("L1 norm of the vector v: ", l2)

Here, v is a vector. We are using the norm() function from numpy.linalg to calculate the L2 norm of vector v. The output of the mentioned program will be:

Vector v: 
 [ 1  2 -3]
L1 norm of the vector v:  3.7416573867739413