In general, for n dimensions, one can write the product of two Levi-Civita symbols as:

Here we just consider objects made up from a finite number k of points in n dimensions.

A projection is a way for representing an n-dimensional object in n 1 dimensions.

An aggregate of n dimensions, to be sure.

Continuing in this way we find such independent Gaussian curvatures for a space of n dimensions.

They generalize in n dimensions as the Pauli matrices.

This means no more than n 1 vectors can be used in n dimensions.

Each grid coordinate stores a gradient of unit length in n dimensions.

The problem becomes analogous to moment of inertia in classical mechanics and is generalizable to n dimensions.

Bivectors are also related to the rotation matrix in n dimensions.