Maximum Dimension of Subspaces with No Product Basis

Yuuya Yoshida

Let $n\ge 2$ and $d_1,\dots ,d_n\ge 2$ be integers, and $\mathcal{F}$ be a field. A vector $u\in {\mathcal{F}}^{d_1}\otimes \cdots \otimes {\mathcal{F}}^{d_n}$ is called a product vector if…