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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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  • Alfred Brauer, A new proof of theorems of Perron and Frobenius on non-negative matrices. I. Positive matrices, Duke Math. J. 24 (1957), 367–378. MR 89824
  • Douglas E. Crabtree, Applications of $M$-matrices to non-negative matrices, Duke Math. J. 33 (1966), 197–208. MR 186677
  • Ky Fan, Note on $M$-matrices, Quart. J. Math. Oxford Ser. (2) 11 (1960), 43–49. MR 117242, DOI https://doi.org/10.1093/qmath/11.1.43
  • Miroslav Fiedler and Vlastimil Pták, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J. 12(87) (1962), 382–400 (English, with Russian summary). MR 142565
  • F. R. Gantmacher and M. G. Kreĭn, Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme, Mathematische Lehrbücher und Monographien, I. Abteilung, Bd. V, Akademie-Verlag, Berlin, 1960 (German). Wissenschaftliche Bearbeitung der deutschen Ausgabe: Alfred Stöhr. MR 0114338

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Article copyright: © Copyright 1966 American Mathematical Society