Let $k$ be a field, let $V$ and $W$ be finite-dimensional vector spaces over $k$, and let $B: V \times W \to k$ be a [bilinear form](/page/Bilinear%20Form). Define the left and right radicals by
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\begin{align*}
\operatorname{rad}_L(B) := \{v \in V : B(v,w)=0 \text{ for every } w \in W\}
\end{align*}
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and
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\begin{align*}
\operatorname{rad}_R(B) := \{w \in W : B(v,w)=0 \text{ for every } v \in V\}.
\end{align*}