Talk:Fiber derivative

Question about "dot"

In the following expression:

$\mathbb {F} L(v)\cdot w={\frac {d}{ds}}|_{s=0}L(v+sw)$

am I to read "$\cdot$" as the natural pairing of a vector and a covector? It doesn't make sense to think of this symbol as the dot (i.e., inner) product of $T^{*}Q$ since $w\in TQ$. (I'd like to clarify the article... just making sure I'm on the right track.)Trevorgoodchild (talk) 19:12, 22 September 2008 (UTC)