论文标题
具有I.I.D的正方形随机矩阵的最小奇异值和条件数。行
Least singular value and condition number of a square random matrix with i.i.d. rows
论文作者
论文摘要
我们考虑了I.I.D.制作的正方形随机矩阵具有任何分布的行，并证明，对于任何给定的维度，最小值值的概率为[0; $ε$）至少是订单$ε$。这使我们能够概括一个结果，即对居中的高斯i.i.d.的状况编号的期望。条目：这种期望总是无限的。此外，对于一些众所周知的随机矩阵集合，我们将获得一些其他结果，尤其是各向同性对数洞穴案例，事实证明，在井条件下，这是最佳行为。
We consider a square random matrix made by i.i.d. rows with any distribution and prove that, for any given dimension, the probability for the least singular value to be in [0; $ε$) is at least of order $ε$. This allows us to generalize a result about the expectation of the condition number that was proved in the case of centered gaussian i.i.d. entries: such an expectation is always infinite. Moreover, we get some additional results for some well-known random matrix ensembles, in particular for the isotropic log-concave case, which is proved to have the best behaving in terms of the well conditioning.
