# Solution: 2020-16 A convex function of matrices

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).

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