# 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 $$(1-\delta, 1+\delta)$$.

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