Definition:Orthogonal (Bilinear Form)

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 $V$.

$v,w\in V$ are orthogonal (with respect to $b$) $b(v,w) = b(w,v) = 0$

This is denoted: $v\perp w$.

Orthogonal Subsets
Let $S,T\subset V$ be subsets.

Then $S$ and $T$ are orthogonal $s\perp t$ for all $s\in S$ and $t\in T$.