The Smallest Singular Value of a Shifted Random Matrix

Xiaoyu Dong

Let $R_n$ be a $n\times n$ random matrix with i.i.d. subgaussian entries. Let $M$ be a $n\times n$ deterministic matrix with norm $\Vert M\Vert \le n^{\gamma }$ where $1/2<\gamma <1$. The g…