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Proceedings of the American Mathematical Society

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Characteristic roots of $ M$-matrices


Author: Douglas E. Crabtree
Journal: Proc. Amer. Math. Soc. 17 (1966), 1435-1439
MSC: Primary 15.25
DOI: https://doi.org/10.1090/S0002-9939-1966-0199203-3
MathSciNet review: 0199203
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  • [1] Alfred T. Brauer, A new proof of theorems of Perron and Frobenius on non-negative matrices, Duke Math. J. 24 (1957), 367-378. MR 0089824 (19:725g)
  • [2] Douglas E. Crabtree, Applications of $ M$-matrices to non-negative matrices, Duke Math J. 33 (1966), 197-208. MR 0186677 (32:4135)
  • [3] Ky Fan, Note on $ M$-matrices, Quart. J. Math (2) 11 (1960), 43-49. MR 0117242 (22:8024)
  • [4] M. Fiedler and V. Ptak, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J. 12 (1962), 382-400. MR 0142565 (26:134)
  • [5] F. R. Gantmacher and M. G. Krein, Oszillationsmatrizen, Oszillationskerne, und kleine Schwingungen mechanischer Systeme, translated by Alfred Stohr, Akademie-Verlag, Berlin, 1960. MR 0114338 (22:5161)

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DOI: https://doi.org/10.1090/S0002-9939-1966-0199203-3
Article copyright: © Copyright 1966 American Mathematical Society

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