The independence conjecture for von Neumann Sylvester matrix rank
Let GGG be a group, let KKK be a field, and let ϕ1,ϕ2:K→C\phi_1,\phi_2:K\to\mathbb{C}ϕ1,ϕ2:K→C be embeddings of KKK into C\mathbb{C}C. For a matrix A∈Matn×m(K[G])A\in\operatorname{Mat}_{n\times m}(K[G])A∈Matn×m(K[G]), writ…