Quadratic space

Radical of a quadratic space

Let be a quadratic space. The radical of is the set of all degenerate vectors, #m/def/linalg i.e.

i.e. the linear kernel of the curried linear map . In particular (away from 2) it is a totally isotropic vector subspace of .

Properties

• Away from 2 all degenerate vectors are isotropic, so any subspace of the radical is a Normal quadratic subspace.

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