Quadratic space

Radical of a quadratic space

Let (𝑉,𝑞) be a quadratic space. The radical rad⁡𝑉 of 𝑉 is the set of all degenerate vectors, linalg i.e.

rad⁡𝑉={𝑣∈𝑉:𝑏𝑞(𝑣,𝑉)=0}

i.e. the linear kernel of the curried linear map 𝑏𝑞 :𝑉 →𝖵𝖾𝖼𝗍𝕂(𝐾,𝑉). In particular (away from 2) it is a ^totallyIsotropic vector subspace of 𝑉.

Properties

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

---

tidy | en | SemBr