Invertibility of random submatrices via tail decoupling and a Matrix Chernoff Inequality

Stéphane Chrétien, Sébastien Darses

Let $X$ be a $n\times p$ matrix with coherence $\mu (X)={\max }_{j\ne j^{\prime }}|X_j^t{X}_{j^{\prime }}|$. We present a simplified and improved study of the quasi-isometry property for most submatrices…