\begin{definition}[Definition:Nondegenerate Symmetric Covariant 2-Tensor]
Let $V$ and $V^*$ be a finite dimensional vector space and its dual.
Let $q$ be a symmetric covariant 2-tensor on $V$.
Let $\hat q : V \to V^*$ be a linear mapping such that:
:$\forall v, w \in V : \map {\map {\hat q} v} w := \map q {v, w}$
Suppose $\hat q$ is an isomorphism.
Then $q$ is said to be '''nondegenerate'''.
\end{definition}