Rank-one covariance spike
= Rank-one covariance spike
{title2=$\Sigma=I+\theta uu^\top$}
For a unit vector $u$ and $\theta>0$, a rank-one covariance spike is the <covariance matrix> $I+\theta uu^\top$. Its <eigenvalue> is $1+\theta$ in the direction $u$ and one on the <orthogonal complement>. It arises by adding an independent scalar <normal distribution> signal $Yu$ to a standard <Gaussian random vector>.