Is the set of matrices $M \in \mathbb{C}^{n \times m}$ for which the first column of $M$ is contained in the span of the other columns of $M$ Zariski closed?
2026-03-27 13:03:22.1774616602
Is it Zariski closed: The set of matrices for which the first column is in the span of the other columns
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The answer in general is "no." When $m=2$ and $n=1$, this is $(\mathbb{C}^2 \setminus V(x_2)) \cup \{(0,0)\}$, which is not Zariski closed.