On families of anticommuting matrices

Pavel Hrubeš

Let $e_1,\dots ,e_k$ be complex $n\times n$ matrices such that $e_i{e}_j=-e_j{e}_i$ whenever $i\ne j$. We conjecture that $\hbox{rk}(e_{1}^{2})+\hbox{rk}(e_{2}^{2})+\cdots…