  Let $\mathbf{A}_{n,m;k}$ be a random $n \times m$ matrix with entries from
some field $\mathbb{F}$ where there are exactly $k$ non-zero entries in each
column, whose locations are chosen independently and uniformly at random from
the set of all ${n \choose k}$ possibilities.
  In a previous paper (arXiv:1806.04988), we considered the rank of a random
matrix in this model when the field is $\mathbb{F}=GF(2)$. In this note, we
point out that with minimal modifications, the arguments from that paper
actually allow analogous results when the field $\mathbb{F}$ is arbitrary.
  In particular, for any field $\mathbb{F}$ and any fixed $k\geq 3$, we
determine an asymptotically correct estimate for the rank of
$\mathbf{A}_{n,m;k}$ in terms of $c,n,k$ where $m=cn/k$, and $c$ is a constant.
This formula works even when the values of the nonzero elements are
adversarially chosen. When $\mathbb{F}$ is a finite field, we also determine
the threshold for having full row rank, when the values of the nonzero elements
are randomly chosen.
