Gaussian empirical Gram matrix
= Gaussian empirical Gram matrix
{c}
{title2=$\widehat\Sigma=G^TG/n$}
For a matrix $G$ with <independent> standard normal entries, $G^TG/n$ is a <Gaussian empirical Gram matrix> and has <expectation> equal to the identity. With mean known to be zero it is the raw empirical second moment. Subtracting a sample mean would give a different estimator. On any fixed unit vector its <quadratic form> is a chi-squared variable divided by $n$.