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 [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

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

How is this generalized to nxn matrices?