The determinant | Chapter 6, Essence of linear algebra

3Blue1Brown · 5M views · 2016-08-10 · 10:03

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Overview

A 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.

On Hacker News

HN repeatedly points people to it as the clearest visual intuition for determinants, often saying it finally made the concept click.

Recommended by 6 HN people across 6 months · HN mentions 2019–2024

Topics

Pure mathematics Recreational & visual math

What people said

traes · 2024-11 · Strong recommendation
The entire 3blue1brown series[0] on linear algebra is well worth watching, it has really intuitive graphical explanations of a bunch of concepts. Here's the one on determinants in particular[1]. TL;DW the determinant represents how much you scale the area/volume/hypervolume (depending on dimension) of a shape by applying a matrix transformation to each point. [0] [LINK] [1] [VIDEO]
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meken · 2023-02 · Strong recommendation
Determinants always fascinated me, partly (completely?) because of the cool sounding name. I always wanted to get intuition for them because their formula is so simple, which has always been deeply unsatisfying to me to just take on its face. This article got me searching for a 3blue1brown video on determinants and now my mind is absolutely blown! [VIDEO]
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MaxBarraclough · 2020-08 · Strong recommendation
At the same time, universities could sometimes do a better job of letting students see why it's important to learn something. A great example is matrix determinant, which at first glance seems like an entirely arbitrary invention. The 3Blue1Brown YouTube channel does a great job with this, introducing the determinant in terms of geometry. It puts the geometric meaning of the function first, introducing the strange looking formula later on. edit And of course, it does all of this with excellent visualisations. [VIDEO]
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Sources

Video by 3Blue1Brown, played through YouTube.

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