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Aequationes mathematicae

, Volume 17, Issue 1, pp 305–310 | Cite as

An inclusion region for the field of values of a doubly stochastic matrix based on its graph

  • Charles R. Johnson
Research papers

AMS (1970) subject classification

Primary 15A42, 15A51, 15A63 

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References

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    Dmitriev, N. andDynkin, E.,On the characteristic numbers of a stochastic matrix. Dokl. Adad. Nauk SSSR49 (1945), 159–162.MathSciNetMATHGoogle Scholar
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    Johnson, C. R.,Gersgorin sets and the field of values. J. Math. Anal. Appl.45 (1974), 416–419.MathSciNetCrossRefMATHGoogle Scholar
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    Johnson, C. R.,Functional characterizations of the field of values and the convex hull of the spectrum. Proc. Amer. Math. Soc61 (1976), 201–204.MathSciNetCrossRefMATHGoogle Scholar
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    Johnson, C. R. andKellogg, R. B.,An inequality for doubly stochastic matrices. J. Res. Nat. Bur. Standards80B (1976), 433–436.MathSciNetMATHGoogle Scholar
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    Karpelevich, F.,On the eigenvalues of a matrix with nonnegative elements. Izv. Akad. Nauk SSR Ser. Mat.15 (1951), 361–383. (Russian).MATHGoogle Scholar
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    Kellogg, R. B.,On complex eigenvalues of M and P matrices. Numer. Math.19 (1972), 170–175.MathSciNetCrossRefGoogle Scholar
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    Kellogg, R. B. andStephens, A.,Complex eigenvalues of a nonnegative matrix with a specified graph. Linear Algebra and Appl. (to appear).Google Scholar
  8. [8]
    Ryser, H.,Combinatorial Mathematics. Carus Monograph No. 14, Wiley and Sons, 1963.Google Scholar

Copyright information

© Birkhäuser Verlag 1978

Authors and Affiliations

  • Charles R. Johnson
    • 1
  1. 1.Department of Economics and Inst. for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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