Suppose that \( f \) is a real-valued convex function on \( \mathbb{R} \). Prove that the function \( X \mapsto \mathrm{Tr } f(X) \) on the vector space of \( N \times N \) Hermitian matrices is convex.

The best solution was submitted by Kook, Yun Bum (국윤범, 수리과학과 2015학번). Congratulations!

Here is his solution of problem 2016-6.

Alternative solutions were submitted by 이종원 (수리과학과 2014학번, +3), 이준호 (2016학번, +3), 장기정 (수리과학과 2014학번, +3), 유현우 (한양대학교 화학공학과 2013학번, +3), 이시우 (포항공대 수학과 2013학번, +3).