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Pré-Publication, Document De Travail Année : 2011

Invertibility of random submatrices via the Non-Commutative Bernstein Inequality

Résumé

Let $X$ be a $n\times p$ matrix. We provide a detailed study of the quasi isometry property for random submatrices of $X$ obtained by uniform column sampling. The analysis relies on a tail decoupling argument with explicit constants and a recent version of the Non-Commutative Bernstein inequality (NCBI) [14]. Our results complement those obtained in [13] for the moments of submatrices. They also generalize and improve on those in [2], which are based on a Non-Commutative Kahane- Kintchine inequality (NCKI).

Dates et versions

hal-00580309 , version 1 (27-03-2011)

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Stéphane Chrétien, Sébastien Darses. Invertibility of random submatrices via the Non-Commutative Bernstein Inequality. 2011. ⟨hal-00580309⟩
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