Let \( A \) be an \( m \times n \) matrix and \( \delta \in (0, 1) \). Suppose that \( \| A^T A – I \| \leq \delta \). Prove that all singular values of \( A \) are contained in the interval \( (1-\delta, 1+\delta) \).

The best solution was submitted by 고성훈 (수리과학과 2018학번). Congratulations!

Here is his solution of problem 2019-21.

A similar solution was submitted by 김태균 (수리과학과 2016학번, +3). Incomplete solutions was submitted by 박재원 (2019학번, +2), 하석민 (수리과학과 2017학번, +2).