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Uniqueness of l1 minimization

Let $A \in \mathbb{R}^{m \times n}$. Is it true that $$\min \limits_{Q \in \mathbb{R}^{n \times m}}|I - QA|_{\infty} < \frac{1}{2}$$ is criteria for the uniqueness of the 1-sparse solution to $\min …
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