Fixed coordinate subspace
= Fixed coordinate subspace
{title2=$\mathbb R_k^p=\{\theta:\theta_j=0\ (j>k)\}$}
The <fixed coordinate subspace> of dimension $k$ in $\mathbb R^p$ consists of vectors whose coordinates after the first $k$ vanish. Restricting a <quadratic form> to it uses only the leading $k$ by $k$ matrix block. It specifies one fixed support; allowing every support of size $k$ would introduce another combinatorial counting step.