Title: The nonnegative rank factorizations of nonnegative matrices
Abstract: Let A ∈ Pm × nr, the set of all m × n nonnegative matrices having the same rank r. For matrices A in Pm × nn, we introduce the concepts of “A has only trivial nonnegative rank factorizations” and “A can have nontrivial nonnegative rank factorizations.” Correspondingly, the set Pm × nn is divided into two disjoint subsets P(1) and P(2) such that P(1)∪P(2) = Pm × nn. It happens that the concept of “A has only trivial nonnegative rank factorizations” is a generalization of “A is prime in Pn × nn.” We characterize the sets P(1) and P(2). Some of our results generalize some theorems in the paper of Daniel J. Richman and Hans Schneider [9].