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> The remarkable thing about quaternions is that you can describe rotation around any arbitrary axis! Try doing that with real rotation matrices and you will bump into a major problem

https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matri...

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I understand you can represent any rotation with matrices, but it's very awkward, and when you compose rotations, you quickly lose information about the resulting axis of rotation.

The information is still there. The axis of rotation is the eigenvector with eigenvalue 1. (That vector doesn't move when you apply the rotation)

Okay let me rephrase: the axis of rotation becomes relatively obfuscated!

I guess it doesn't matter if you're doing everything on the computer, but it's pretty cool that with quarternions you can immediately see the composite rotation's axis and angle without any extra work!

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