# Restricted Invertibility Revisited

@article{Naor2017RestrictedIR,
title={Restricted Invertibility Revisited},
author={Assaf Naor and Pierre Youssef},
journal={arXiv: Functional Analysis},
year={2017},
pages={657-691}
}
• Published 5 January 2016
• Mathematics
• arXiv: Functional Analysis
Suppose that $$m,n \in \mathbb{N}$$ and that $$A: \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$$ is a linear operator. It is shown here that if $$k,r \in \mathbb{N}$$ satisfy $$k <r\leqslant \mathbf{rank}(A)$$ then there exists a subset σ ⊆ {1, …, m} with | σ | = k such that the restriction of A to $$\mathbb{R}^{\sigma } \subseteq \mathbb{R}^{m}$$ is invertible, and moreover the operator norm of the inverse $$A^{-1}: A(\mathbb{R}^{\sigma }) \rightarrow \mathbb{R}^{m}$$ is at most a constant…
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