VC dimension of a vector space
= VC dimension of a vector space
{c}
The sign class of a $d$-dimensional real <vector space> of functions has VC dimension at most $d$. If $n>d$ points were shattered, the <linear map>[evaluation map] from the function space to $\mathbb R^n$ would have a nonzero vector orthogonal to its image. Choosing labels according to the signs of that vector contradicts orthogonality.