%0 Journal Article
%T On families of anticommuting matrices
%A Pavel Hrube£¿
%J Computer Science
%D 2014
%I arXiv
%X Let $e_{1},\dots, e_{k}$ be complex $n\times n$ matrices such that $e_{i}e_{j}=-e_{j}e_{i}$ whenever $i\not=j$. We conjecture that $\hbox{rk}(e_{1}^{2})+\hbox{rk}(e_{2}^{2})+\cdots+\hbox{rk}(e_{k}^{2})\leq O(n\log n)$, and prove some results in this direction.
%U http://arxiv.org/abs/1412.5893v1