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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Factorizations of nonnegative matrices


Author: T. L. Markham
Journal: Proc. Amer. Math. Soc. 32 (1972), 45-47
MSC: Primary 15.60
DOI: https://doi.org/10.1090/S0002-9939-1972-0289539-2
MathSciNet review: 0289539
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Abstract: 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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DOI: https://doi.org/10.1090/S0002-9939-1972-0289539-2
Keywords: Factorization, nonnegative matrix, almost principal minor, lower triangular matrix, upper triangular matrix
Article copyright: © Copyright 1972 American Mathematical Society