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Let $A = (a_{ij})$ be a square $n\times n$ matrix with i.i.d. zero mean andunit variance entries. Rudelson and Vershynin showed that the upper bound for asmallest singular value $s_n(A)$ is of order $n^{-\frac12}$ with probabilityclose to one under additional assumption on entries of $A$ that$\mathbb{E}a^4_{11} < \infty$. We remove the assumption on the fourth momentand show the upper bound assuming only $\mathbb{E}a^2_{11} = 1.$

An upper bound on the smallest singular value of a square random matrix