The symmetric representation of lines in $\text{PG}({\mathbb{F}}^3\otimes {\mathbb{F}}^3)$

Michel Lavrauw, Tomasz Popiel

Let $\mathbb{F}$ be a finite field, an algebraically closed field, or the field of real numbers. Consider the vector space $V={\mathbb{F}}^3\otimes {\mathbb{F}}^3$ of $3\times 3$ mat…