The Spinor Norm
The spinor norm is a homomorphism from an orthogonal group over a field F to F*/F*2 (the multiplicative group of the field F up to square elements), that takes reflection in a vector of norm n to the image of n in F*/F*2.
For the usual orthogonal group over the reals it is trivial, but it is often non-trivial over other fields, or for the orthogonal group of a quadratic form over the reals that is not positive definite.
Read more about this topic: Orthogonal Group
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