Let A∈R≥0M×NA\in\mathbb{R}_{\geq 0}^{M\times N}A∈R≥0M×N have non-negative rank H0H_0H0, and suppose that A=U0V0A=U_0V_0A=U0V0 for some strictly positive matrices U0∈R>0M×H0U_0\in\mathbb{R}_{>0}^{M\times H_0}U0∈R>0M×H0 and…