Definition:Nondegenerate Symmetric Covariant 2-Tensor
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Definition
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.
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Pseudo-Riemannian Metrics