Let $k$ be a field, let $V$ and $W$ be finite-dimensional vector spaces over $k$ with $\dim_k V = \dim_k W = n$, and let
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\begin{align*}
B: V \times W \to k
\end{align*}
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be a [bilinear form](/page/Bilinear%20Form). Fix bases $(v_1,\dots,v_n)$ of $V$ and $(w_1,\dots,w_n)$ of $W$, and let $A = (a_{ij}) \in k^{n \times n}$ be the matrix of $B$ in these bases, defined by
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\begin{align*}
a_{ij} = B(v_i,w_j).
\end{align*}
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Then $B$ is nondegenerate, meaning that both radicals
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\begin{align*}
\{v \in V : B(v,w)=0 \text{ for all } w \in W\}
\end{align*}
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and
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\begin{align*}
\{w \in W : B(v,w)=0 \text{ for all } v \in V\}
\end{align*}