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Characteristic polynomial splits into linear factors

  1. Sep 18, 2008 #1
    Is it true that the characteristic polynomial of an n by n matrix over GF(q) splits into linear factors over GF(q^n)?

    I see that it must do if the polynomial is irreducible but what if it isn't?
  2. jcsd
  3. Sep 19, 2008 #2


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    Let p be an irreducible polynomial of degree k over GF(q). What does the splitting field of p (over GF(q)) look like?
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