Definition:Orthogonal (Bilinear Form)/Radical

Definition

Let $\mathbb K$ be a field.

Let $V$ be a vector space over $\mathbb K$.

Let $b : V\times V \to \mathbb K$ be a reflexive bilinear form on $V$.

The radical of $V$ is the orthogonal complement of $V$:

$\operatorname{rad}(V) = V^\perp$

Also see

• Definition:Degenerate Bilinear Form