"Determine if the following quadratic form is positive definite, negative definite or undefinite
$Q:\mathbb R^3\to \mathbb R, \,Q(u)=x_1^2+4x_1x_2-2x_2^2+2x_1x_3-2x_3^2$"
$Q=\begin{bmatrix} 1&2&1 \\\ 2&-2&0 \\\ 1&0&-2 \end{bmatrix}$
- I tried to compute the diagonal matrix but the eigenvalues are not integers, thus it's a bit hard to calculate by hand. UPDATE: Seemingly, I've done something wrong previously.
- I tried to group them to form squares, however there is nothing that guarantees is either positive or negative. Plugging in numbers results in both positive and negative results.
- What else to try?