Definition:Orthogonal (Bilinear Form)/Subsets

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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 $V$.

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

Then $S$ and $T$ are orthogonal if and only if for all $s\in S$ and $t\in T$, $s$ and $t$ are orthogonal: $s \perp t$.