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Characteristic polynomial coefficients

  1. Sep 29, 2011 #1
    For any characteristic polynomial determined from A - eI (where A is a nxn matrix, e is an eigenvalue and I is the identity matrix),

    is it a rule that the coefficient associated with the char. polynomail term of highest degree must be positive ?

    My tutor made a theory that if the characteristic polynomial's coefficient of highest power is negative, then divide it through by -1 to make it positive.

    Im not sure why it has to be positive, so I'd really like some clarification

    thanks
     
  2. jcsd
  3. Sep 29, 2011 #2

    mathwonk

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    there is no rule on this. there is an annihilator ideal and the characteristic polynomial is any generator, so the first coefficient could almost be anything. i usually like it to be positive. but if you define it to be a certain determinant t could be either. this is not at all important for applications.
     
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