## Determinant of a symmetric matrix

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
$$A(x) = $\left( \begin{array}{ccc} f(x) & a_{12}(x) & a_{13}(x) \\ a_{12}(x) & f(x) & a_{23}(x) \\ a_{13}(x) & a_{23}(x) & f(x) \end{array} \right)$$$

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

Krindik
 PhysOrg.com science news on PhysOrg.com >> King Richard III found in 'untidy lozenge-shaped grave'>> Google Drive sports new view and scan enhancements>> Researcher admits mistakes in stem cell study
 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor Hi Krindik! If we define a vector B = (B1, B2, B3) = (a23, a31, a12), then the determinant is f(x)3 - B2f(x)
 Thanks :)

## Determinant of a symmetric matrix

 Quote by 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)
How is this generalized to nxn matrices?