Nonnegative factorization of positive semidefinite nonnegative matrices

Abstract

We give simple geometric proofs of the known results that, for n ≤4, n × n nonnegative positive semidefinite matrices can be factored into n × n nonnegative factors and that, for n ≥ 5, these conditions are not sufficient to guarantee the existence of such a factorization. © 1980.