Let $A$ be an $ntimes n$ symmetric positive definite matrix with eigenvalues and eigenvectors $lambda_1gelambda_2gecdotsgelambda_n>0$ and $v_1,v_2,cdots,v_n$ respectively.

Then we know that the largest eigenvalue of $A$ can be obtained by “trace maximization” or “Rayleigh quotient maximization”.

I also noted that the largest eigenvalue of $A$ can be obtained by minimizing $|A-xx’|_F^2$. Specifically, $x=pm sqrtlambda_1 v_1$ are minimizers of $minlimits_{xinmathbb{R}^n} |A-xx’|_F^2$.

So I am wondering is there a specific name for this optimization problem or if you could direct me to some literature. Thanks!