How to calculate the L1 norm of a vector using Python?

by | Oct 3, 2023 | Linear Algebra

L1-norm

What is the L1 norm of a vector?

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

L^q=||\vec{v}||_q=(\sum_{k}{|v_k|^q})^{\frac{1}{q}}

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

L^1=||\vec{v}||_1=(\sum_{k}{|v_k|})

In other words, if we take the absolute value of each component of a vector and sum them up, we will get the L1 norm of the vector. The L1 norm is also called the Manhattan norm.

Let’s look at an example. Let’s say v is a vector as given below:

\vec{v}=\begin{bmatrix} 1 \\ 2 \\ -3 \end{bmatrix}

So, the L1 norm of the vector v will be:

L^1=||\vec{v}||_1=(\sum_{k}{|v_k|})=|1|+|2|+|-3|=6

How to calculate the L1 norm of a vector using Python?

We can use the following Python code to calculate the L1 norm of a vector using NumPy…

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Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

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