On the eigenvalues of matrices

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Let A be an n×n matric with arbitrary complex elements and with eigen-values λ1, λ2, ..., λn. A method is described for the approximàte determination of max | λj | ; characteristical is that prescribing a percentual error the number of elementary operations of the process, necessary to reach such precision, depends only on n and not on the elements of A More general characteristical equations are also considered.


  1. (1)

    P. Turàn,Eine neue Methode in der Analysis und deren Anwendungen, Budapest, 1953.

  2. (2)

    J. W. S. Cassels,On the sums of powers of complex numbers, « Acta Math. Hung. T. VII. », fasc. 3–4 (1957) p. 283–290.

  3. (3)

    F. V. Atkinson,On power-sums of complex numbers. « In print in Acta Math. Hung. ».

  4. (4)

    J. N. Franklin,On numerical solution of characteristic equations in flutter-analysis « J. Assoc. Comput. Mach. 5 (1958) p. 45–51.

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To Enrico Bompiani on his scientific Jubilee

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Turàn, P. On the eigenvalues of matrices. Annali di Matematica 54, 397–401 (1961) doi:10.1007/BF02415365

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  • Elementary Operation
  • Arbitrary Complex
  • Complex Element
  • Characteristical Equation
  • Percentual Error