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How can we define the Inner Product of multi-variable functions?

For example, what is the value of the inner product of $\nabla f$ and $\nabla g$?

$$\langle \nabla f, \nabla g\rangle = ?? $$

Here $\langle\cdot,\cdot\rangle$ is used for the inner product in $L^2$.

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    $\langle \nabla f, \nabla g\rangle_{L^2(\Omega)} = \sum_i \int_\Omega \partial_i f\, \partial_i g\, dx$.2012-04-21
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    @martini As I expected! Thanks a lot.2012-04-21
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    @Ashuley Use '\langle \rangle' which gives $\langle \rangle$ instead of $<>$.2012-04-21
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    @martini How about $\langle f, g \rangle \text{where} f(x,y) \text{and } g(x,y)$? Thanks2018-09-07

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