Linear rank preservers of tensor products of rank one matrices

Zejun Huang, Shiyu Shi, Nung-Sing Sze

Let $n_1,\dots ,n_k$ be integers larger than or equal to 2. We characterize linear maps $\varphi :M_{n_1\cdots n_k}\to M_{n_1\cdots n_k}$ such that $${\mathrm rank}\,(ϕ(A_1\otim…