The nonnegative rank factorizations of nonnegative matrices (Q2266051)

Suppose A is an \(m\times n\) matrix. If \(A=BC\) where A, B, C are nonnegative (elementwise) matrices, and rank A\(=\) rank B\(=\) rank C, then BC is a nonnegative (full) rank factorization of the nonnegative matrix A. This paper characterizes when A has nontrivial nonnegative rank factorizations. Special attention is paid to the case when rank A\(<\min \{m,n\}\).