Large affine spaces of non-singular matrices
Large affine spaces of non-singular matrices
Let $\mathbb {K}$ be an arbitrary (commutative) field with at least three elements. It was recently proven that an affine subspace of $\operatorname {M}_n(\mathbb {K})$ consisting only of non-singular matrices must have a dimension less than or equal to $\binom {n}{2}$. Here, we classify, up to equivalence, the subspaces whose …