Euler Vector Fields - MathOverflow

Euler Vector Fields [closed]

I have the following question:

If $(x^1,\ldots,x^n)$ are the standard coordinates on $R^n$ and $(y^1,\ldots,y^n)$ are other coordinates on $R^n$, how can we show that $\sum x^i\frac{\partial}{\partial x^i} =\sum y^i\frac{\partial}{\partial y^i}$ ?

Thank you!

flag	asked Nov 20 2011 at 18:43 Louis 1

	You look at how the LHS acts on a linear combination of x's, how the RHS acts on a linear combination of y's and then remember that those are the same thing. – Ben Webster♦ Nov 20 2011 at 18:58
	That said, I don't think this question is really appropriate for MO. Even if it isn't HW, it's at the level of an undergraduate HW, which is not what MO is for. You might try math.stackexchange.com – Ben Webster♦ Nov 20 2011 at 19:00