Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 31L / c / Solution

Only the symmetric part of $M$ contributes to $x^{T}Mx$. The functionstherefore form a real vector space of dimensionwith coordinates given by the quadratic monomials $x_i^2$ and $x_i{x}_j$ for $i<j$. The theorem on signs of a finite-dimensional function space says that the sign class of a $D$-dimensional real vector space has VC dimension at most $D$. Consequently