Positive matrix factorization via extremal polyhedral cones (Q1963935)

Let \(A,\) \(B,\) and \(C\) be positive \(k\times m,\) \(k\times n,\) and \(n\times m\) matrices, respectively, such that \(A=BC.\) The least integer \(n\) for which such a factorization of \(A\) exists is called the positive matrix rank of \(A.\) The authors reduce the search for the factorization of a positive matrix to the search for an embedding of a polyhedral cone in either an extremal polyhedral cone or in a facet of the positive orthant.