1. Quadratic Forms - Reduction Techniques

hi all,

i am trying to do an assignment here and i would like to verify my answer to the following question:

Let $Q=x_1^2+2x_2^2-7x_3^2-4x_1x_2+8x_1x_3$
Find a non-singular matrix $P$ and a diagonal matrix $D=diag(d_1,d_2,d_3)$ such that Q is transformed to $Q'=d_1y_1^2+d_2y_2^2+d_3y_3^2$; under the transformation $X=PY$

2. Re: Quadratic Forms - Reduction Techniques

i used the congruence method of reduction and i ended up with

$D=diag(1, 4, -288)$

and $P=\left(\begin{array}{ccc}1&0&-8\\0&4&28\\0&2&16\end{array}\right)$