= Affine hyperplane
{title2=$H=\{v\in V:\ell(v)=c\},\quad\ell\ne0$}
In a finite-dimensional real vector space, a level set of a nonzero <linear functional> is an affine hyperplane. Choosing $v_0$ in that level set gives $H=v_0+\ker\ell$, so its dimension is one less than that of the ambient space. With a Euclidean inner product, translation followed by an orthonormal basis of $\ker\ell$ identifies it isometrically with the lower-dimensional Euclidean space. The coordinate-sum constraint on balanced cut vectors is an example.
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