We show that a nearly square independent and identically distributed random integral matrix is surjective over the integral lattice with very high probability. This answers a question by Koplewitz [6]. Our result extends to sparse matrices as well as to matrices of dependent entries.

中文翻译：

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近方随机矩阵的超射性

我们证明了一个几乎平方独立且同分布的随机积分矩阵以非常高的概率在积分格上是满射的。这回答了 Koplewitz [6] 的一个问题。我们的结果扩展到稀疏矩阵以及依赖项的矩阵。