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Determinant of a symmetric matrix

  1. Mar 5, 2010 #1
    Hi,

    Is there a simplification for the determinant of a symmetric matrix? For example, I need to find the roots of [tex] \det [A(x)] [/tex]
    where
    [tex]
    A(x) = \[ \left( \begin{array}{ccc}
    f(x) & a_{12}(x) & a_{13}(x) \\
    a_{12}(x) & f(x) & a_{23}(x) \\
    a_{13}(x) & a_{23}(x) & f(x) \end{array} \right)\]
    [/tex]

    Really appreciate if you could point me in the correct directions. Thanks in advance,

    Krindik
     
  2. jcsd
  3. Mar 6, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Krindik! :smile:

    If we define a vector B = (B1, B2, B3) = (a23, a31, a12),

    then the determinant is f(x)3 - B2f(x) :wink:
     
  4. Mar 7, 2010 #3
    Thanks :)
     
  5. Dec 18, 2010 #4
    How is this generalized to nxn matrices?
     
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