Let $A$ be an $n \times n$ Hermitian matrix and $\lambda_1 (A) \geq \lambda_2 (A) \geq \dots \geq \lambda_n (A)$ the eigenvalues of $A$. Prove that for any $1 \leq k \leq n$
$$A \mapsto \lambda_1 (A) + \lambda_2 (A) + \dots + \lambda_k (A)$$
is a convex function.

The best solution was submitted by 채지석 (수리과학과 2016학번). Congratulations!

Here is his solution of problem 2020-16.

Other solutions were submitted by 길현준 (수리과학과 2018학번, +3), 이준호 (수리과학과 2016학번, +3).