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On limits of the real characteristic roots of matrices with real elements


Author: Gene W. Medlin
Journal: Proc. Amer. Math. Soc. 7 (1956), 912-917
MSC: Primary 15.0X
DOI: https://doi.org/10.1090/S0002-9939-1956-0085219-8
MathSciNet review: 0085219
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  • [1] Alfred Brauer, Limits for the characteristic roots of a matrix II, Duke Math. J. vol. 14 (1947) pp. 21-26.
  • [2] -, Limits for the characteristic roots of a matrix III, Duke Math. J. vol. 15 (1948) pp. 8.71-977.
  • [3] -, Limits for the characteristic roots of a matrix IV: Applications to stochastic matrices, Duke Math. J. vol. 19 (1952) pp. 75-91.
  • [4] -, Limits for the characteristic roots of a matrix V, Duke Math. J. vol. 19 (1952) pp. 553-562.
  • [5] Alfred Brauer, Über die Lage der charakteristischen Wurzeln einer Matrix, J. Reine Angew. Math. 192 (1953), 113–116 (German). MR 0059237, https://doi.org/10.1515/crll.1953.192.113
  • [6] -, Bounds for the ratios of the co-ordinates of the characteristic vectors of a matrix, Proc. Nat. Acad. Sei. U.S.A. vol. 41 (1955) pp. 162-164.
  • [7] J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math. 30 (1906), no. 1, 175–193 (French). MR 1555027, https://doi.org/10.1007/BF02418571
  • [8] T. Bonnesen and W. Fenchel, Theorie der Konvexen Körper, New York, Chelsea, 1958.

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DOI: https://doi.org/10.1090/S0002-9939-1956-0085219-8
Article copyright: © Copyright 1956 American Mathematical Society