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 associated left and right linear maps by
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\begin{align*}
L_B: V \to W^*, \qquad L_B(v)(w) = B(v,w)
\end{align*}
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for $v \in V$ and $w \in W$, and
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\begin{align*}
R_B: W \to V^*, \qquad R_B(w)(v) = B(v,w)
\end{align*}