Proceedings of the American Mathematical Society · 1972 · 17 citations · 3 references
ComputingData ScienceAlgebraRepresentation TheorySeparation Of PowersMatrix ComputationMatrix FactorizationMatrix StructureNon-negative Matrix FactorizationPositive DefinitenessPositive Matrix FactorizationRank-revealing FactorizationsReal Numbers
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.
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