Irrationality of linear combinations of eigenvectors

  • Anthony Manning


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.


Irrationality Galois group eigenvectors 


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Copyright information

© Indian Academy of Sciences 1995

Authors and Affiliations

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

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