\begin{definition}[Definition:Discriminant of Bilinear Form]
Let $\mathbb K$ be a field.
Let $V$ be a vector space over $\mathbb K$ of finite dimension $n>0$.
Let $b : V\times V \to \mathbb K$ be a bilinear form on $V$.
Let $A$ be the matrix of $b$ relative to an ordered basis of $V$.
If $b$ is nondegenerate, its '''discriminant''' is the equivalence class of the determinant $\det A$ in the quotient group $\mathbb K^\times / (\mathbb K^\times)^2$.
If $b$ is degenerate, its '''discriminant''' is $0$.
\end{definition}