Determinant of a symmetric matrix

  • Thread starter krindik
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  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
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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:
 
  • #3
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Thanks :)
 
  • #4
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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:
How is this generalized to nxn matrices?
 

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