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arXiv · 2108.05413

The Smallest Singular Value of a Shifted Random Matrix

Xiaoyu Dong
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Abstract

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 $\lVert M \rVert \le n^\gamma$ where $1/2<\gamma<1$. The goal of this paper is to give a general estimate of the smallest singular value of the sum $R_n + M$, which improves an earlier result of Tao and Vu.

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Xiaoyu Dong. 2021-08-11. The Smallest Singular Value of a Shifted Random Matrix. https://arxiv.org/abs/2108.05413

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