Irrationality of linear combinations of eigenvectors
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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.
KeywordsIrrationality Galois group eigenvectors
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