Gaussian elimination in a glimpse

Joseph Salmon

Author

Joseph Salmon

Published

September 9, 2025

Gaussian elimination

Here is a simple visualisation of the Gaussian elimination steps:

and a more complete one:

For more details, the Python source code is available here: https://github.com/josephsalmon/Tweets/tree/master/Pivot_Gauss_video

Citation

BibTeX citation:

@online{salmon2025,
  author = {Salmon, Joseph},
  title = {Gaussian Elimination in a Glimpse},
  date = {2025-09-09},
  url = {https://josephsalmon.eu/blog/gaussian_elimination/},
  langid = {en}
}

---
title: "Gaussian elimination in a glimpse"
author:
  - name: Joseph Salmon
    url: https://josephsalmon.eu/
    orcid: 0000-0002-3181-0634
date: "2025-09-09"
description: "Gaussian elimination in action: a simple visualization of a famous algorithm "
categories: [linear algebra, math visualization]
image: "gaussian_elimination.gif"
reference-location: document
fig-cap-location: bottom
draft: false
---

# Gaussian elimination

Here is a simple visualisation of the Gaussian elimination steps:
<img src="https://raw.github.com/josephsalmon/Tweets/master/Pivot_Gauss_video/gauss_pivot.gif" title="Evolution of a random square matrix along the steps of a Gaussian elimination" style="width:100%" />

and a more complete one:
<img src="https://raw.github.com/josephsalmon/Tweets/master/Pivot_Gauss_video/gauss_pivot_4figs.gif" title="Evolution of a random square matrix along the steps of a Gaussian elimination: on the top left you have the transvection matrix used at each step, on the top right the original matrix, on the bottom left the matrix display the approximation of the inverse matrix, on the bottom right the remaining extra-diagonal terms of the matrix that need to be canceled to find the inverse." style="width:100%" />

For more details, the Python source code is available here: [https://github.com/josephsalmon/Tweets/tree/master/Pivot_Gauss_video](https://github.com/josephsalmon/Tweets/tree/master/Pivot_Gauss_video)