Suppose I have a rank one positive semidefinite matrix $V = vv^T$, how to find $v$ efficiently?
$v\in\mathbb{R}^n$
I know the diagonal term $v_1^2, \ldots,v_n^2$ will tell me something; however, we have to choose $\pm$ sign. Also we can consider other terms to help us; however, if $n$ is large, how to find $v$ efficiently? (particularly when writing it in a code.)