Cochran's theorem
= Cochran's theorem
{c}
{wiki}
Orthogonal projections of an isotropic Gaussian vector are independent. If $P$ is an orthogonal projection of rank $r$ and $Z\sim N(0,I)$, then
$$
\|PZ\|^2\sim\chi_r^2.
$$
= Cochran's theorem
{c}
{wiki}
Orthogonal projections of an isotropic Gaussian vector are independent. If $P$ is an orthogonal projection of rank $r$ and $Z\sim N(0,I)$, then
$$
\|PZ\|^2\sim\chi_r^2.
$$