# Determinant of a symmetric matrix

1. Mar 5, 2010

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

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

Krindik

2. Mar 6, 2010

### 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)

3. Mar 7, 2010

### krindik

Thanks :)

4. Dec 18, 2010

### yiorgos

How is this generalized to nxn matrices?