Important 4D spaces:
Simulate it. Just simulate it.
Video 1.
4D Toys: a box of four-dimensional toys by Miegakure (2017)
. Source.
This section is about the definition of the dot product over , which extends the definition of the dot product over .
The complex dot product is defined as:
E.g. in :
We can see therefore that this is a form, and a positive definite because:
Just like the usual dot product, this will be a positive definite symmetric bilinear form by definition.
Given:
the norm ends up being:
E.g. in :
with extra structure added to make it into a metric space.
Each elliptic space can be modelled with a real projective space. The best thing is to just start thinking about the real projective plane.

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