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Proceedings of the American Mathematical Society

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



Nonnegative matrices with nonnegative inverses

Author: Ralph DeMarr
Journal: Proc. Amer. Math. Soc. 35 (1972), 307-308
MSC: Primary 15A48
MathSciNet review: 0296089
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Abstract: We generalize a result stating that a nonnegative finite square matrix has a nonnegative inverse if and only if it is the product of a permutation matrix by a diagonal matrix. We consider column-finite infinite matrices and give a simple proof using elementary ideas from the theory of partially ordered linear algebras.

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  • [1] T. A. Brown, M. Juncosa and V. Klee, Invertibly positive linear operators on spaces of continuous functions, Math. Ann. 183 (1969), 105-114. MR 42 #8314. MR 0273436 (42:8314)
  • [2] R. E. DeMarr, Convergence of a sequence of powers, Proc. Amer. Math. Soc. 23 (1969), 401-403. MR 39 #6805. MR 0245497 (39:6805)

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Keywords: Matrix theory, inverses, ordered algebras
Article copyright: © Copyright 1972 American Mathematical Society

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