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Quadratic forum

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    i have quadratic form
    [tex]x^2-xy+y^2[/tex]
    how can I check if this form has always same sign (+ or -)?
     
  2. jcsd
  3. Feb 23, 2010 #2
    It's non-negative for all x,y, and 0 only at 0,0. Suppose |x|<|y|. Then |xy|<y^2, and the expression is positive. Likewise if |y|<|x|.
     
  4. Feb 28, 2010 #3
    i heard about silvester method (with det), how i can solve this with this method?
     
  5. Feb 28, 2010 #4

    Dick

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    Represent the form as a matrix, M, so x^(T)Mx is your quadratic form. Then find the eigenvalues of M.
     
  6. Feb 28, 2010 #5
    well, I know that:) but why this form is represented by this matrix? why this form is defined when its more than 0 and no defined when less? and what can I do when det is 0?
     
  7. Feb 28, 2010 #6

    Dick

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    I think the answers would be a lot clearer if you actually tried to do the problem. What is the matrix M and what are it's eigenvalues? It only has two and they are both positive.
     
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