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).