So I have the quadratic form $Q(x,y,z)=x^2+y^2-z^2$.
I now would like to obtain its corresponding bilinear map.
Now I've studied Sylvesters' theorem which says that any symmetric bilinear map $B$ is determined uniquely by its quadratic form. It also says that you can obtain the bilinear map from the polarization identity.
I am not sure how to obtain the bilinear map from here. I do know that, according to my notes,
$B(v,v)=Q(v)$ where $Q:V \to R^3$ and $v ∈ V$.
How do I obtain the bilinear form from $B(v,w):=\frac{1}{2}(Q(v+w)-Q(v)-Q(w))$? (using this polarization equation is given as a hint)
Thank you in advance.