Nonnegative matrices with nonnegative inverses
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- by Ralph DeMarr
- Proc. Amer. Math. Soc. 35 (1972), 307-308
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296089-6
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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.References
- T. A. Brown, M. Juncosa, and V. Klee, Invertibly positive linear operators on spaces of continuous functions, Math. Ann. 183 (1969), 105–114. MR 273436, DOI 10.1007/BF01350230
- R. E. DeMarr, Convergence of a sequence of powers, Proc. Amer. Math. Soc. 23 (1969), 401–403. MR 245497, DOI 10.1090/S0002-9939-1969-0245497-8
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 307-308
- MSC: Primary 15A48
- DOI: https://doi.org/10.1090/S0002-9939-1972-0296089-6
- MathSciNet review: 0296089