Factorizations of nonnegative matrices
Thomas L. Markham · Proceedings of the American Mathematical Society · 1972
Suppose A is an n-square matrix over the real numbers such that all principal minors are nonzero. If A is nonnegative, then necessary and sufficient conditions are determined for A to be factored into a product $L \cdot U$, where L is a lower triangular nonnegative matrix and U is an upper triangular nonnegative matrix with ${u_{ii}} = 1$. These conditions are given in terms of the nonnegativity of certain almost-principal minors of A.