= Polar bilinear form of a quadratic form
{title2=$B_Q(x,y)=Q(x+y)-Q(x)-Q(y)$}
The displayed <bilinear form> is the polar form of a <quadratic form>. In odd <characteristic of a field>, $Q(x)=B_Q(x,x)/2$ recovers the <quadratic form>; in <characteristic of a field> two, different forms can have the same <alternating bilinear form>. Over $\mathbb F_2$, two such forms differ by a <linear map> to the <field>, giving the affine parametrization of <binary quadratic refinements>.
Back to article page