Geometric algebra MOC

Quotient quadratic space

Let be a quadratic space and be a normal subspace. The quotient quadratic space is the corresponding quotient vector space with the (well-defined) quadratic form #m/def/geoalg

Properties

  1. The quotient vector space has a well-defined quadratic form iff is a normal normal subspace.
Proof of 1.

For the quadratic form to be well defined, we require for all and . Equivalently

for all and . This includes, however, that , so any such must be both degenerate and isotropic.

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