Vectors | Chapter 1, Essence of linear algebra

3Blue1Brown · 13M views · 2016-08-06 · 9:52

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Overview

The first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.

On Hacker News

HN's go-to recommendation for learning linear algebra intuition, repeatedly credited with making concepts click and complementing textbooks.

Recommended by 17 HN people across 18 months · HN mentions 2018–2026

Topics

Pure mathematics Recreational & visual math

What people said

zvmaz · 2026-07 · Strong recommendation
3Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified. [1] [VIDEO]
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seanhunter · 2025-11 · Strong recommendation
If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but extremely superficial. If you're done with 3b1b and want to take things further, then the go-to is the excellent 18.06SC course by the late and legendary Gilbert Strang. It's amazing, it's free. [2] Still want more? OK now you're talking my language. If you are serious about linear algebra (Up to graduate level, after that you need something else) then you want the book "Linear Algebra Done Right" by Sheldon Axler. It's available for free from the author's website[3] and he has made a bunch of videos to supplement the book. There's also an RTD Math full lecture series[4] that follows the book and he explains each thing in a lot of detail (because Axler goes fast , so it's beneficial to unpack the concepts a bit sometimes). [1] [VIDEO] [2] [LINK] [3] [LINK] and [LINK] [4] [LINK]
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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] [VIDEO] [1] [LINK]
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Sources

Video by 3Blue1Brown, played through YouTube.

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