News for hackers. Stuff that matters.

A comment on Quaternion Knowledge Graph Embeddings. Parent comment

Re:Quaternion Knowledge Graph Embeddings by aap_ on Thursday April 25, 2024 @04:33AM (#40154955)
> Quaternions? Well that's about 4D

Quaternions are about 3D. You need 4 numbers for it, but the space that they operate on is 3D.

[ Parent | on HN ]
Re:Quaternion Knowledge Graph Embeddings by raincole on Thursday April 25, 2024 @05:11AM (#40155191)
He's talking from a mathematical perspective, not a compute graphics one.

(Unit) quaternions happens to work as rotations in 3D space. But quaternions' algebraic structure is indeed 4D, just like imaginary numbers' is 2D.

[ Parent | on HN ]
Re:Quaternion Knowledge Graph Embeddings by ducttapecrown on Thursday April 25, 2024 @01:42PM (#40160689)
Since you can multiply a quaternion by a quaternion, the quaternions act on themselves, so they indeed act on a 4D space. They can also act on a couple 3D spaces: the unit sphere in 4D, called the three sphere, or the imaginary quaternions.

In math, this is called a representation of a Lie group, and there are representations in all dimensions.

[ Parent | on HN ]