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Hessian matrix

  1. Dec 27, 2008 #1
    g(x,y) = x^3 - 3x^2 + 5xy -7y^2

    Hessian Matrix =



    Now I have to find the eigenvalues of this matrix, so I end up with the equation (where a = lambda)

    (6x - 6 - a)(-7 - a) - 25 = 0

    Multiplying out I get:

    a^2 - 6xa + 13a - 42x + 17 = 0

    How am I supposed to solve for a? Usually I just use the quadratic formula for my eigenvalues..

    Should I take a third row/ column for my hessian matrix?
  2. jcsd
  3. Dec 27, 2008 #2

    D H

    Staff: Mentor

    First off, you have a numerical error in your Hessian. Double check your derivation.

    To find the eigenvalues, just solve for a as you would normally (i.e., the eigenvalues will be functions of x).
  4. Dec 27, 2008 #3

    That's the whole question, I assume I'm doing something wrong because my roots of the quadratic for lamba is very complicated.

    And yes thankyou I changed my -7 value in my hessian for -14
  5. Dec 27, 2008 #4

    D H

    Staff: Mentor

    So, what is H(0,0)?
  6. Dec 27, 2008 #5
    I've no idea :D this is the 1st hessian question ive ever done, i also previosuly made a thread in the same section about what this notation meant, because I'm not too sure.

    Do I just plug in x= 0 and y=0?

    So my hessian would be:


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