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Irrationality of linear combinations of eigenvectors

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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.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK

    Anthony Manning

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  1. Anthony Manning
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Manning, A. Irrationality of linear combinations of eigenvectors. Proc. Indian Acad. Sci. (Math. Sci.) 105, 269–271 (1995). https://doi.org/10.1007/BF02837192

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  • DOI: https://doi.org/10.1007/BF02837192

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