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Irrationality of linear combinations of eigenvectors

  • Anthony Manning
Article

Abstract

A givenn ×n matrix of rational numbers acts onC π and onQ π. We assume that its characteristic polynomial is irreducible and compare a basis of eigenvectors forC π with the standard basis forQ π. Subject to a hypothesis on the Galois group we prove that vectors from these two bases are as independent of each other as possible.

Keywords

Irrationality Galois group eigenvectors 

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References

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    Garling D,A course in Galois theory (Cambridge: University Press) (1986)MATHGoogle Scholar
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    Smale S, Differentiable dynamical systems,Bull. Am. Math. Soc. 73 (1967) 747–817MathSciNetCrossRefGoogle Scholar
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    Walters P,An introduction to ergodic theory (New York: Springer) (1982)MATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 1995

Authors and Affiliations

  • Anthony Manning
    • 1
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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