Why can't you multiply vectors?

Freya Holmér · 524.6K views · 2023-10-26 · 51:16

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Overview

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

On Hacker News

HN treats it as the best entry point to geometric algebra and an intuitive route to understanding quaternions.

Recommended by 9 HN people across 5 months · HN mentions 2023–2025

Topics

Pure mathematics Recreational & visual math Game programming & engines

What people said

gowld · 2024-08 · Strong recommendation
The absolute first video to watch should be the (ironically titled) Why can't you multiply vectors? [VIDEO]
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zoogeny · 2024-02 · Strong recommendation
One of my favorite math/graphics YouTube creators Freya Holmér did an excellent intro to Geometric Algebra not that long ago [1]. If you have any interest in 3d graphics (especially but no limited to splines/Bezier curves) then be sure to check out all of their videos. I personally have always struggled with linear algebra and I tend to find these Clifford Algebra approaches much more intuitive. 1. [VIDEO]
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simpaticoder · 2024-02 · Strong recommendation
In another comment, they pointed out [VIDEO] in which Freya did an excellent job reducing the number of axioms to 1: If you define multiplying a vector by itself to be equal to the length of the vector, squared, then everything else falls out of simple polynomial multiplication. It's quite lovely.
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Sources

Video by Freya Holmér, played through YouTube.

HN Library · Source license

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