(adsbygoogle = window.adsbygoogle || []).push({}); Got the theorem, having trouble with the proof... [SOLVED]

Hi all. OK, so I am trying to prove a theorem that I have for some time been just using as-is. Long story short, it occured to me that I needed to prove it. So, I have almost done it, but am stuck near the end. The theorem is:

Suppose [itex] \mathcal{X} [/itex] is a smooth vector field on a manifold [itex]\mathcal{M}[/itex]. Assuming that [itex]\mathcal{X}_p\neq0[/itex] at a point [itex]p\in\mathcal{M}[/itex], then there exists a coordinate neighborhood [itex]\left(\mathcal{W};w^i\right)[/itex] about [itex]p[/itex] such that

[tex]

\left.\mathcal{X}\right\vert_\mathcal{W}=\dfrac{\partial}{\partial w^1}

[/tex]

Proof: ????

Now, it's not that I have nothing for the proof, it's just that I'm stuck. As well, since there is more than one way to skin a cat, I figured it would be better to leave the proof empty, rather than potentially confuse anyone with the technique I have employed thus far.

That said, a big thanks in advance for all the help!

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# Got the theorem, having trouble with the proof

**Physics Forums | Science Articles, Homework Help, Discussion**