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Generalization of inequalities by carmichael and mason and by parodi

Verallgemeimerung von Ungleichungen von Carmichael und Mason und von Parodi

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Abstract

We find upper bounds for the latent roots of a λ-matrix. The bounds obtained are, for complex polynomials, the classical ones of Carmichael and Mason and Parodi.

Zusammenfassung

Wir leiten obere Schranken für die Eigenwerte von λ-Matrizen her. Für komplexe Polynome erhält man die klassischen Schranken von Carmichael und Mason und von Parodi.

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References

  1. Carmichael, R. D., Mason, T. E.: Note on the roots of algebraic equations. Bull. Amer. Math. Soc.21, 14–22 (1914).

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  2. Deutsch, E.: Matricial norms. Numer. Math.16, 73–84 (1970).

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  3. Mitrinovic, D. S.: Analytic inequalities. Berlin-Heidelberg-New York: Springer 1970.

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  4. Parodi, M.: La localisation des valeurs caractéristiques des matrices et ses Applications. Paris: Gauthier-Villars 1959.

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  5. Robert, F.: Sur les normes vectorielles régulières sur un espace de dimension finie. C.R.A.S. Paris261, 5173–5176 (1965).

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  6. Vitória, J.: Normas vectoriais de vectores e de matrizes. Report, Univ. Lourenç Marques (Mozambique), 1974.

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Authors and Affiliations

  1. Instituto de Matemática Faculadade de Ciências e Technologia, Universidade de Combra, 3000, Coimbra, Portugal

    J. Vot'oria

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  1. J. Vot'oria
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Additional information

Much of the research for this note was done while the author was at the Department of mathematics, Universidade Eduardo Mondlane, Maputo, People's Republic of Mozambique.

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Vot'oria, J. Generalization of inequalities by carmichael and mason and by parodi. Computing 22, 363–365 (1979). https://doi.org/10.1007/BF02265316

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  • DOI: https://doi.org/10.1007/BF02265316

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