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).