# eigenvalues – Is there a specific name for this optimization problem?

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!