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Recognizing cyclic matrices and a conjecture of J.G. Thompson | | John D. Dixon
; | | Date: |
7 Jun 2016 | | Abstract: | In 2006 J.G. Thompson conjectured: "If F is a field and A is in GL(n,F), then
there is a permutation matrix P such that AP is cyclic, that is, the minimal
polynomial of AP is also its characteristic polynomial" (open problem 16.95 in
the Kourovka Notebook). The present note provides a simple criterion for a
matrix to be cyclic and uses this to prove Thompson’s conjecture. | | Source: | arXiv, 1606.2238 | | Services: | Forum | Review | PDF | Favorites | |
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