I read:
The bilinear form $(Dg)^{-1}[a](Dg)^{-T}[a]$ is positive definite on the tangent space $T_a S$ uniformly in $a \in S$
where $g:S\subset \mathbb{R}^n \to T \subset \mathbb{R}^n$.
I don't understand what the bilinear form is.. and how can it be defined on the tangent space? does the map $(Dg)^{-1}[a](\cdot)$ go from $S \to T$ or am I wrong?