How to calculate the Euclidean distance between two matrices using Python?

by | Oct 3, 2023 | Featured, Linear Algebra

Euclidean Distance Between Matrices

How to calculate the Euclidean distance between two matrices?

Let A and B be two mxn matrices. And Ai,j and Bi,j be the element in the ith row and jth column of the matrix A and B, respectively. The Euclidean distance between these two matrices A and B is defined as:

||A-B||_F=\sqrt{\sum_{i=1}^{m}{\sum_{j=1}^{n}{|A_{i,j}-B_{i,j}|^2}}}

For example, let’s say A and B are the following two matrices:

A=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \\ B=\begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}

So, the Euclidean distance between A and B will be:

||A-B||_F=\sqrt{\sum_{i=1}^{m}{\sum_{j=1}^{n}{|A_{i,j}-B_{i,j}|^2}}} \\ =\sqrt{(1-5)^2+(2-6)^2+(3-7)^2+(4-8)^2} \\ =\sqrt{4^2+4^2+4^2+4^2}=8

How to calculate the Euclidean distance between two matrices using Python?

We can use the following Python code to calculate the Euclidean distance between two matrices…

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Amrita Mitra

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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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