This page identifies the Clifford group within a Clifford algebra and provides code to compute a real matrix which performs the same transformation as the group element.

Transformations that preserve non-positive definite quadratic forms are mentioned near the end of this. Here we provide code for such modified Clifford algebras. We have not combined these two tricks yet but it should be easy.

Here is a program to compute random indefinite orthogonal matrices.

Here we show how to uses these matrices to define the entire group of isometries in a uniformly curved space.