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> A quaternion is basically a 4 dimensional vector, so it has a magnitude (or norm, or length) Is it really a vector in the physical sense? People often say ve
by captainmuon 5y ago
> A quaternion is basically a 4 dimensional vector, so it has a magnitude (or norm, or length)
Is it really a vector in the physical sense? People often say vector when they mean N-tuple -- for example we learned in high school that vectors are just N numbers taken together.
For physicists, a vector must satisfy certain transformation laws - it must transform in the correct way if a rotation is applied, and the scalar product must be invariant of the coordinate system, IIRC. I don't have enough intuition of quaternions to say how they behave under transformations, though. I would be surprized if you could have "proper" vectors with four components in three-dimensional space.
- marosgrego 5y agoIt's a vector in the mathematical sense.
- foo92691 5y agoWell, quaternions form a vector space over quaternion addition. This part is not very interesting. Vector spaces do not describe multiplication of vectors by each other. So, quaternions are not (only) vectors "in the mathematical sense" when it comes to their more interesting properties.
- marosgrego 5y agoWhat do you mean? They also form an algebra (a vector space where a "multiplication" is defined).
- littlestymaar 5y agoA vector is a member of a vector space. A vector space is a set V + a Field F, where for all x,y in V and a in F, x + ay is also in V. That's it.