On families of anticommuting matrices

الأصل · EN

Let e₁,, eₖ be complex n× n matrices such that eᵢeⱼ=-eⱼeᵢ whenever i=j. We conjecture that rk(e₁²)+rk(e₂²)++rk(eₖ²)≤ O(n n), and prove some results in this direction.