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edited body

edited Mar 9 at 1:12

Low rank matrix in a subspace of matrices

Let $V\subset M_{m,n}(\mathbb{C})$ be a $n$-dimensional subspace ($m\geq 2$). Is there $X\in V$ such that $1\leq \mathrm{rank}\, X\leq m-1$?

asked Mar 9 at 0:44