Hello.(adsbygoogle = window.adsbygoogle || []).push({});

How can I show the Divergence of a vector field is a scalar field(in [tex]E^{3}[/tex]) ?

Should I show that Div is invariant under rotation?

[tex]x^{i'}=a^{ij}x^{j},V^{'}_{i}(\stackrel{\rightarrow}{x})=a_{ij}v_{j}(\stackrel{\rightarrow}{x})[/tex]

then

[tex]\frac{\partial V^{'}_{i}(\stackrel{\rightarrow}{x})}{\partial x^{'i}}=\frac{\partial(a_{ij}V_{j} (\stackrel{\rightarrow}{x})) }{\partial(a^{ij} x^{j} ) } = \frac{\partial V_{i} (\stackrel{\rightarrow}{x})}{\partial x^{i}} [/tex]

How can I prove the last equality?

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

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Divergence of a vector field is a scalar field?

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