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Why can't you multiply vectors?

Freya HolmérYouTube ↗

Further reading 1

What does a matrix do, and which outputs can disappear? →Read a column as an arrow, then a matrix as an action on that arrow. Solving an equation becomes a question about reachable targets, giving collapse, eigenvectors and rotations a geometric interpretation.This video helps answer · What does multiplying a vector mean?

Caption notes

Starting from a vector whose square equals its squared length, the talk derives a product with scalar and oriented-plane parts and connects it to rotations.

Original passages · 4
multiplying two vectors together is the dot product plus the wedge product
Why can't you multiply vectors? · ▶ 38:21–38:37
we interpret it as a bi Vector so it's an oriented plane with an area and and that's it
Why can't you multiply vectors? · ▶ 35:43–35:56
this returns a b Vector it generalizes to any Dimension it doesn't have to be only 3D
Why can't you multiply vectors? · ▶ 38:00–38:13
natural numbers are closed under addition and multiplication
Why can't you multiply vectors? · ▶ 10:28–10:35

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