# Solution: 2019-21 Approximate isometry

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).

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