Determinant of a symmetric matrix

[krindik]

Hi,

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

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

Krindik

 

[tiny-tim]

Hi Krindik!

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

then the determinant is f(x)³ - B²f(x)

 

[krindik]

Thanks :)

 

[yiorgos]

Hi Krindik!

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

then the determinant is f(x)³ - B²f(x)

How is this generalized to nxn matrices?