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Homework Help: Inconclusive Hessian

  1. Jul 19, 2010 #1
    What is the general approach to take when the Hessian is inconclusive when classifying critical points? ie the determinant = 0?
     
  2. jcsd
  3. Jul 19, 2010 #2
    If det(H) = 0 and H has both positive and negative eigenvalues at x, then x is a saddle point for the function.

    If not...then classifying degenerate critical points [det(H) = 0] becomes quite difficult from what I know. Thom's Splitting Lemma might work. It's sort of a parametrized version of the Morse lemma.
    http://en.wikipedia.org/wiki/Splitting_lemma_(functions [Broken])

    In general, I think it's safe to say that degenerate critical points are annoying haha.
     
    Last edited by a moderator: May 4, 2017
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