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When do polynomials maintain similarity? Does this result from Cayley–Hamilton theorem?

Similar matrices have the same eigenvalues, but for instance $A$ and $A-\lambda I$ don't have the same eigenvalues. The later has $A$'s eigenvalues shifted by $\lambda$.

I'm missing something here.

  • 3
    Similarity is respected by addition and raise to power, so it is preserved by any polynomial.2012-11-07
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    But does that follow from the Cayley–Hamilton theorem?2012-11-07
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    I'm not sure what you mean by polynomials maintain similarity, but in any case Cayley–Hamilton is a far deeper fact and has nothing to do with this.2012-11-07
  • 0
    http://math.stackexchange.com/questions/161637/similar-matrices-and-equivalence-relations2012-11-07

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