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Visualizing the 4d numbers Quaternions

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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 · How do rotations change in four dimensions?

Caption notes

Stereographic projection makes unit quaternions visible. Left multiplication rotates two perpendicular planes together, distinct from the conjugation used for three-dimensional orientation.

Original passages · 4
everything you're looking at really has the same magnitude
Visualizing the 4d numbers Quaternions · ▶ 22:06–22:21
two separate 2D rotations, happening perpendicular to and in sync with each other
Visualizing the 4d numbers Quaternions · ▶ 23:19–23:34
One thing worth noticing here is that order of multiplication matters.
Visualizing the 4d numbers Quaternions · ▶ 28:40–28:43
knowing what our transformation does to them gives us the full information about what it does to all of space
Visualizing the 4d numbers Quaternions · ▶ 25:32–25:44

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