\begin{definition}[Definition:Nondegenerate Subspace of Scalar Product Space]
Let $\struct {V, q}$ be a scalar product space.
Let $S \subseteq V$ be a subspace.
Suppose the restriction of $q$ to $S \times S$ is nondegenerate, where $\times$ denotes the cartesian product.
Then $S$ is said to be '''nondegenerate'''.
\end{definition}