# Is there a specific name for this optimization problem?

Let $$A$$ be an $$n\times n$$ symmetric positive definite matrix with eigenvalues and eigenvectors $$\lambda_1\ge\lambda_2\ge\cdots\ge\lambda_n>0$$ and $$v_1,v_2,\cdots,v_n$$ respectively.

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 via

$$\underset{x \in \mathbb{R}^n}{\text{minimize}} \quad \|A-xx'\|_F^2 \tag{OP}$$

Specifically, $$x = \pm \sqrt \lambda_1 v_1$$ are minimizers of $$\text{(OP)}$$.

Is there a specific name for this optimization problem? Could you please direct me to some literature. Thanks!